1.
The Indian middle class consist of so many strata that it defies categorisation under a single term class, which would imply a considerable degree of homogeneity. Yet two paradoxical features characterise its conduct fairly uniformly; extensive practice and intensive abhorrence of corruption.
In the several recent surveys of popular perceptions of corruptions, politicians of course invariably and understandably top the list, closely followed by bureaucrats, policemen, lawyers, businessmen and others. The quintessential middle class. If teachers do not figure high on this priority list, it is not for lack of trying, but for lack of oppurtunities. Over the years, the sense of shock over acts of corruption in the middle class has witnessed a steady decline, as its ambitions for a better material life have soared but the resources for meeting such ambitions have not kept pace.
What is fascinating, however, is the intense yearning of this class for a clean corruptionless politics and society, a yearning that has again and again surfaced with any figure public or obscure, focus on his mission of eradicating corruption. Even the repeated failure of this promise on virtually every man's part has not subjected it to the law of diminishing returns.
2.
Write a paragraph about " The happiest day in you life "
3.
A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Correct Answer
B. 6 litres, 6 litres
Explanation
To find the solution, let's assume that the milk vendor mixes x liters of milk from the first can and y liters of milk from the second can.
From the first can, since it contains 25% water, the remaining 75% is milk. So, the amount of milk from the first can is 0.75x liters.
From the second can, since it contains 50% water, the remaining 50% is milk. So, the amount of milk from the second can is 0.5y liters.
According to the given ratio, the amount of water to milk should be 3:5. So, the amount of water from the first can is 0.25x liters and the amount of water from the second can is 0.5y liters.
Since the total amount of milk required is 12 liters, we have the equation: 0.75x + 0.5y = 12.
Also, since the ratio of water to milk is 3:5, we have the equation: 0.25x + 0.5y = (3/8) * 12.
Solving these two equations simultaneously, we find that x = 6 liters and y = 6 liters. Therefore, the milk vendor should mix 6 liters of milk from each of the containers to get 12 liters of milk with a water to milk ratio of 3:5.
4.
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
Correct Answer
C. 4 hours
Explanation
The boat's speed in still water is 13 km/hr, and the speed of the stream is 4 km/hr. When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the stream. Therefore, the boat's speed downstream is 13 km/hr + 4 km/hr = 17 km/hr. To find the time taken by the boat to go 68 km downstream, we divide the distance by the speed: 68 km / 17 km/hr = 4 hours.
5.
In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Correct Answer
C. 8 KMPH
Explanation
The speed of the boat in still water can be found by taking the average of the speeds of the boat along the stream and against the stream. In this case, the boat goes 11 km/hr along the stream and 5 km/hr against the stream. The average of these two speeds is (11+5)/2 = 8 km/hr. Therefore, the speed of the boat in still water is 8 km/hr.
6.
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Correct Answer
A. 2.4 KM
Explanation
The man is rowing against the current on his way to the place, so his effective speed is 5 kmph - 1 kmph = 4 kmph. It takes him 1 hour to row to the place, so the distance is 4 kmph x 1 hour = 4 km. On his way back, he is rowing with the current, so his effective speed is 5 kmph + 1 kmph = 6 kmph. It also takes him 1 hour to row back, so the distance is 6 kmph x 1 hour = 6 km. The total distance is the sum of the distances traveled to and from the place, which is 4 km + 6 km = 10 km. However, since the question asks for the distance to the place, we divide the total distance by 2, resulting in 10 km / 2 = 5 km. Therefore, the correct answer is 2.4 km.
7.
A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
Correct Answer
A. 1 KMPH
Explanation
The man rows to a place 48 km distant and comes back in 14 hours. This means that the total distance traveled by the man is 96 km (48 km to the place and 48 km back). Let's assume the speed of the man in still water is x km/h and the speed of the stream is y km/h.
We are given that the man can row 4 km with the stream in the same time as 3 km against the stream. This means that the time taken to row 4 km with the stream is equal to the time taken to row 3 km against the stream.
Using the formula Time = Distance/Speed, we can set up the following equations:
4/(x+y) = 3/(x-y)
Cross multiplying, we get:
4(x-y) = 3(x+y)
Simplifying the equation, we get:
4x - 4y = 3x + 3y
Rearranging the terms, we get:
x = 7y
We also know that the total time taken is 14 hours, so we can set up another equation:
48/(x+y) + 48/(x-y) = 14
Substituting x = 7y into the equation, we get:
48/(8y) + 48/(6y) = 14
Simplifying the equation, we get:
6 + 8 = 14
Therefore, the speed of the stream (y) is 1 km/h. Hence, the correct answer is 1 KMPH.
8.
If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
Correct Answer
A. 48 paise
Explanation
If a quarter kg of potato costs 60 paise, it means that 250 grams of potato costs 60 paise. To find out how many paise 200 grams of potato will cost, we can set up a proportion.
250 grams / 60 paise = 200 grams / x paise
Cross-multiplying, we get:
250x = 60 * 200
Simplifying, we find:
x = (60 * 200) / 250 = 48 paise
Therefore, 200 grams of potato will cost 48 paise.
9.
An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth?
Correct Answer
B. 195
Explanation
The loom weaves 0.128 metres of cloth every second. To find out how many seconds it will take to weave 25 metres of cloth, we can divide 25 by 0.128. This gives us approximately 195 seconds. Therefore, it will take approximately 195 seconds for the loom to weave 25 metres of cloth.
10.
A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
Correct Answer
C. 155 Degrees
Explanation
From noon to 5 o'clock, the hour hand has moved 5 hours, which is equivalent to 30 degrees per hour. At 10 minutes past 5, the hour hand has moved an additional 10 minutes, which is 1/6th of an hour. So, the hour hand has moved a total of 5 hours and 1/6th of an hour, which is equivalent to 5.1666 hours. Therefore, the hour hand has turned through 5.1666 multiplied by 30 degrees, which equals 155 degrees.
11.
The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
Correct Answer
B. 75 Degrees
Explanation
At 8:30, the minute hand is pointing at the 6 on the clock face, while the hour hand is pointing halfway between the 8 and the 9. This means that the hour hand is slightly past the 8. The angle between the minute hand and the hour hand can be calculated by finding the difference between their positions on the clock face. Since the minute hand is at 6 and the hour hand is slightly past 8, the angle between them is 75 degrees.
12.
A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?
Correct Answer
B. 2 p.m. on Wednesday
Explanation
The watch gains 2 minutes in 7 days. So, the watch gains (2/7) minutes per day. From Monday noon to the following Monday 2 p.m., there are 6 days and 26 hours, which is equivalent to 6 days and (26*60) minutes. The watch gains (6*24 + 26*60)*(2/7) minutes in this duration. To find when the watch is correct, we need to subtract this gained time from 2 p.m. on the following Monday. After the calculation, we find that the watch will be correct at 2 p.m. on Wednesday.
13.
What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?
Correct Answer
C. Rs. 10123.20
Explanation
The compound interest can be calculated using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is Rs. 25,000, the rate of interest is 12% (0.12), the number of times interest is compounded per year is 1, and the number of years is 3. Plugging these values into the formula, we get A = 25000(1 + 0.12/1)^(1*3) = Rs. 10123.20.
14.
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Correct Answer
D. 6.09%
Explanation
The effective annual rate of interest is higher than the nominal rate because interest is compounded semi-annually. To calculate the effective annual rate, we use the formula: (1 + (nominal rate/number of compounding periods))^number of compounding periods - 1. In this case, the nominal rate is 6% per annum and it is compounded semi-annually, so the number of compounding periods is 2. Plugging these values into the formula, we get (1 + (0.06/2))^2 - 1 = 0.0609 or 6.09%. Therefore, the correct answer is 6.09%.
15.
The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
Correct Answer
A. 8
Explanation
The difference between compound interest and simple interest is given as Rs. 96. This means that the compound interest is Rs. 96 more than the simple interest. Since the time period is 2 years and the principal amount is Rs. 15,000, we can use the formula for compound interest and simple interest to find the rate of interest. By substituting the given values and solving the equations, we find that the rate of interest per annum is 8%.
16.
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
Correct Answer
C. 42, 33
Explanation
The correct answer is 42, 33. This answer satisfies the given conditions where one student secures 9 marks more than the other and his marks are 56% of the sum of their marks. In this case, 42 is 9 marks more than 33, and 42 is 56% of the sum of 42 and 33.
17.
Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Correct Answer
D. 4 : 6
Explanation
The given question states that the sum of 5% of A and 4% of B is two-thirds of the sum of 6% of A and 8% of B. Let's assume the values of A and B to be 4x and 6x respectively.
According to the given information, (5/100) * 4x + (4/100) * 6x = (2/3) * [(6/100) * 4x + (8/100) * 6x]
Simplifying the equation, we get 0.2x + 0.24x = (2/3) * (0.24x + 0.48x)
0.44x = (2/3) * 0.72x
0.44x = 0.48x
0.04x = 0
This equation is not possible as it results in 0 = 0. Therefore, the given question is incomplete or not solvable.
18.
Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Correct Answer
C. Rs. 19.70
Explanation
The total cost of the items purchased is Rs. 25. The sales tax on taxable purchases is 30 paise, which is 6% of the cost of taxable items. Therefore, the cost of taxable items is (30 paise * 100) / 6 = Rs. 5. The cost of tax-free items can be calculated by subtracting the cost of taxable items from the total cost of items purchased, which is Rs. 25 - Rs. 5 = Rs. 20. However, the question asks for the cost of tax-free items, so we need to subtract the sales tax from the cost of tax-free items. Therefore, the cost of tax-free items is Rs. 20 - Rs. 0.30 = Rs. 19.70.
19.
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Correct Answer
C. 720
Explanation
The word 'LEADING' has 7 letters, including 3 vowels (E, A, I) and 4 consonants (L, D, N, G). To arrange the letters in such a way that the vowels always come together, we can treat the group of vowels as a single entity. Thus, we have 4 entities to arrange: the group of vowels (EAI), L, D, N, and G. The number of ways to arrange these entities is 4!, which is equal to 24. However, within the group of vowels, the vowels can be arranged in 3! ways. Therefore, the total number of arrangements is 24 * 3!, which is equal to 720.
20.
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Correct Answer
D. 209
Explanation
In order to find the number of different ways to select four children from a group of 6 boys and 4 girls, we can use the concept of combinations. We need to calculate the number of combinations with at least one boy.
To do this, we can calculate the total number of combinations of selecting four children from the group (10C4) and subtract the number of combinations with no boys (4C4).
10C4 = (10!)/(4!(10-4)!) = 210
4C4 = (4!)/(4!(4-4)!) = 1
Therefore, the number of combinations with at least one boy is 210 - 1 = 209.
21.
In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
A. 32 B. 48
C. 36 D. 60
E. 120
Correct Answer
C. 36
Explanation
The word 'DETAIL' has 6 letters. Since the vowels (E, A, I) need to occupy only the odd positions, we can consider them as a single unit. So, we have 4 units to arrange: D, T, L, and the vowel unit (EAI). The number of ways to arrange these 4 units is 4!. However, within the vowel unit, there are 3 vowels that can be arranged among themselves in 3! ways. Therefore, the total number of arrangements is 4! * 3! = 24 * 6 = 144. However, we need to divide this by 2 since the vowels (EAI) can be arranged among themselves in 2! ways. Therefore, the final number of arrangements is 144 / 2 = 72. Since the question asks for the number of ways the letters can be arranged such that the vowels occupy only the odd positions, we need to divide this by 2 again to account for the fact that the consonants can also be arranged among themselves in 2! ways. Therefore, the final answer is 72 / 2 = 36.
22.
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Correct Answer
B. 720
Explanation
The word 'OPTICAL' has 7 letters, including 3 vowels (O, I, A) and 4 consonants (P, T, C, L). To arrange the letters such that the vowels always come together, we can consider the group of vowels as a single entity. This entity can be arranged in 3! = 6 ways. Within this entity, the vowels can be arranged in 3! = 6 ways. The remaining 4 consonants can be arranged in 4! = 24 ways. Therefore, the total number of arrangements is 6 * 6 * 24 = 720.
23.
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Correct Answer
A. 24
Explanation
Let's assume that Sameer's present age is 5x and Anand's present age is 4x. According to the given information, 3 years from now, Sameer's age will be 5x+3 and Anand's age will be 4x+3. The ratio of their ages at that time will be 11:9. Therefore, we can set up the equation (5x+3)/(4x+3) = 11/9. By solving this equation, we find that x = 3. Substituting x = 3 into Anand's present age, we get 4x = 4*3 = 12. Therefore, Anand's present age is 12 years.
24.
At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
Correct Answer
B. 15 Years
Explanation
Let's assume the present age of Arun is 4x and the present age of Deepak is 3x. After 6 years, Arun's age will be 4x+6=26 years. Solving this equation, we find that x=5. Therefore, the present age of Deepak is 3x=3*5=15 years.
25.
Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
Correct Answer
D. Data Inadequate
Explanation
The question provides information about the sum of the ages of R and T, but it does not provide any specific information about the ages of Q, R, or T individually. Without knowing the individual ages of Q, R, and T, it is not possible to determine the difference between R and Q's age. Therefore, the answer is Data Inadequate.
26.
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
Correct Answer
D. 16
Explanation
The six bells toll at intervals of 2, 4, 6, 8, 10, and 12 seconds respectively. To find the number of times they toll together in 30 minutes, we need to find the least common multiple (LCM) of these intervals. The LCM of 2, 4, 6, 8, 10, and 12 is 120. Since there are 60 minutes in 30 minutes, the bells will toll together every 120 seconds. In 30 minutes, there are 30 x 60 = 1800 seconds. Dividing 1800 by 120 gives us 15. Therefore, the bells will toll together 15 times in 30 minutes.
27.
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
Correct Answer
A. 40
Explanation
The given numbers are in the ratio of 3 : 4 : 5. Let's assume the numbers to be 3x, 4x, and 5x. The LCM of these numbers is 2400. So, we can write the equation as 3x * 4x * 5x = 2400. Solving this equation, we get x = 4. Therefore, the numbers are 12, 16, and 20. The HCF of these numbers is 4. Hence, the correct answer is 40.
28.
Find the lowest common multiple of 24, 36 and 40.
Correct Answer
C. 360
Explanation
The lowest common multiple (LCM) is the smallest number that is divisible by all the given numbers. To find the LCM of 24, 36, and 40, we can list the multiples of each number and find the smallest number that appears in all three lists. The multiples of 24 are 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, ... The multiples of 36 are 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, ... The multiples of 40 are 40, 80, 120, 160, 200, 240, 280, 320, 360, ... The smallest number that appears in all three lists is 360, so the correct answer is 360.
29.
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
Correct Answer
C. 308
Explanation
The question is asking for the other number when one of the numbers is given as 275. The highest common factor (H.C.F.) of the two numbers is 11, which means that both numbers are divisible by 11. The least common multiple (L.C.M.) of the two numbers is 7700. Since 275 is one of the numbers and it is divisible by 11, the other number must also be divisible by 11. Looking at the answer choices, only 308 is divisible by 11. Therefore, the other number is 308.
30.
252 can be expressed as a product of primes as:
Correct Answer
A. 2 x 2 x 3 x 3 x 7
Explanation
252 can be expressed as a product of primes as 2 x 2 x 3 x 3 x 7. This is the correct answer because it is the only option that includes all the prime factors of 252 (2, 3, and 7) and their respective exponents. The other options either have missing prime factors or incorrect exponents, making them incorrect.
31.
The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
Correct Answer
D. 548
Explanation
To find the least number that leaves a remainder of 8 when divided by 12, 15, 20, and 54, we need to find the least common multiple (LCM) of these numbers. The LCM of 12, 15, 20, and 54 is 540. Adding 8 to this number gives us 548, which is the least number that satisfies the given conditions. Therefore, the correct answer is 548.
32.
If one-third of one-fourth of a number is 15, then three-tenth of that number is:
Correct Answer
D. 54
Explanation
If one-third of one-fourth of a number is 15, it means that (1/3) * (1/4) * x = 15, where x is the number. Simplifying this equation, we get (1/12) * x = 15. To find three-tenths of the number, we multiply the number by (3/10). Therefore, (3/10) * x = (3/10) * (12/1) * 15 = 54. Hence, the correct answer is 54.
33.
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Correct Answer
B. 24
Explanation
The number must be a two-digit number with a product of 8, meaning the digits must be 2 and 4. When 18 is added to the number, the digits are reversed. Therefore, the number must be 42.
34.
In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Correct Answer
A. 24
Explanation
Let's assume the tens digit of the number is x and the units digit is y. According to the given information, y = x + 2. The number can be represented as 10x + y. The sum of its digits is x + y. So, the equation becomes (10x + y)(x + y) = 144. Substituting y = x + 2, we get (10x + (x + 2))(x + (x + 2)) = 144. Simplifying this equation, we get (11x + 2)(2x + 2) = 144. Solving this quadratic equation, we find x = 2 and y = 4. Therefore, the number is 24.
35.
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
Correct Answer
B. 253
Explanation
The number has 3 digits and the sum of these digits is 10. The middle digit is equal to the sum of the other two digits, which means that it must be 5. If we reverse the digits of the number, we get a new number that is 99 greater than the original number. The only number that satisfies these conditions is 253.
36.
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Correct Answer
B. 50 KMPH
Explanation
The man is running in the same direction as the train, so his speed needs to be subtracted from the speed of the train to calculate the relative speed. The length of the train is given as 125 m, and it takes 10 seconds for the train to completely pass the man. Using the formula speed = distance/time, we can calculate the relative speed as 125/10 = 12.5 m/s. To convert this to km/hr, we multiply by 3.6. Therefore, the relative speed is 12.5 * 3.6 = 45 km/hr. Since the man's speed is 5 km/hr, the speed of the train is 45 + 5 = 50 km/hr.
37.
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Correct Answer
B. 89 SEC
Explanation
The train takes 24 seconds to pass a pole, which means its speed is 240/24 = 10 m/s. To pass a platform 650 m long, the train needs to cover a total distance of 240 + 650 = 890 m. Since its speed is 10 m/s, it will take 890/10 = 89 seconds to pass the platform.
38.
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Correct Answer
C. 36 SEC
Explanation
The jogger is running at a speed of 9 kmph, which is slower than the train's speed of 45 kmph. The train is also longer than the distance between the jogger and the engine, so it will take some time for the train to completely pass the jogger. To find the time it takes for the train to pass the jogger, we can use the formula: time = distance/speed. The distance the train needs to cover to pass the jogger is the sum of the length of the train (120 meters) and the distance between the jogger and the engine (240 meters), which is 360 meters. The speed of the train is given as 45 kmph, which is equivalent to 45000 meters per hour. Plugging these values into the formula, we get time = 360/45000 = 0.008 hours. Converting this to seconds, we get 0.008 * 3600 = 28.8 seconds, which is approximately 36 seconds. Therefore, the train will pass the jogger in 36 seconds.
39.
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Correct Answer
D. 10.8
Explanation
The time taken for the trains to cross each other can be calculated using the formula: time = distance/speed. The total distance that needs to be covered for the trains to cross each other is the sum of their lengths, which is 140m + 160m = 300m. The relative speed of the trains is the sum of their individual speeds, which is 60 km/hr + 40 km/hr = 100 km/hr = 100000/3600 m/s = 250/9 m/s. Plugging these values into the formula, we get time = 300m / (250/9 m/s) = 300 * 9 / 250 = 10.8 seconds.
40.
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Correct Answer
B. 350 m
Explanation
The train takes 18 seconds to cross a signal pole, which means it covers the distance of its own length in that time. Therefore, the length of the train is 300 meters. When the train crosses the platform, it takes 39 seconds, which includes the time it takes to cross the train as well as the platform. So, the extra time taken to cross the platform is 39 - 18 = 21 seconds. Since the train covers the distance of its own length in 18 seconds, the extra time of 21 seconds is used to cover the length of the platform. Therefore, the length of the platform is 300 + 21 = 321 meters.
41.
Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
Correct Answer
B. 24 sec
Explanation
The time taken by the slower train to pass the driver of the faster train can be calculated using the relative speed of the two trains. The relative speed is the sum of their individual speeds. In this case, the relative speed is 45 km/hr + 30 km/hr = 75 km/hr.
To convert the relative speed from km/hr to m/s, we divide it by 3.6 (since 1 km/hr = 1000 m/3600 s = 5/18 m/s). Therefore, the relative speed is 75 km/hr * (5/18 m/s) = 25/2 m/s.
The distance that the slower train needs to cover to pass the driver of the faster train is 500 m (the length of the faster train).
Using the formula distance = speed * time, we can rearrange it to time = distance / speed. Plugging in the values, we get time = 500 m / (25/2 m/s) = 500 m * (2/25 s/m) = 40 s.
However, since we are interested in the time taken by the slower train, which has a slower speed, we need to divide the time by the ratio of their speeds. The ratio of their speeds is 30 km/hr / 45 km/hr = 2/3.
Therefore, the time taken by the slower train to pass the driver of the faster train is 40 s * (2/3) = 80/3 s, which is approximately equal to 26.67 s.
Since the given answer options are in whole seconds, the closest option is 24 sec.
42.
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Correct Answer
B. 50 M
Explanation
The train overtakes the first person in 9 seconds while traveling at a relative speed of 2 kmph. Therefore, the distance covered by the train in 9 seconds is 9 * (2/3600) = 0.05 km. Similarly, the train overtakes the second person in 10 seconds while traveling at a relative speed of 4 kmph. Therefore, the distance covered by the train in 10 seconds is 10 * (4/3600) = 0.0111 km. The difference in distance covered between the two overtakings is the length of the train. Therefore, the length of the train is 0.05 km - 0.0111 km = 0.0389 km = 38.9 m = 39 m. However, the given options do not include 39 m, so the closest option is 50 m.
43.
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Correct Answer
B. 4 : 3
Explanation
The ratio of their speeds is 4:3. This can be determined by considering the time it takes for each train to reach its destination after they meet. Since the first train takes 9 hours to reach its destination and the second train takes 16 hours, we can conclude that the second train is slower. Therefore, the ratio of their speeds is 4:3, with the first train being faster.
44.
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Correct Answer
A. 2000
Explanation
Let's assume the cost price of the article is x.
Given that the percentage profit earned by selling the article for Rs. 1920 is equal to the percentage loss incurred by selling it for Rs. 1280, we can set up the following equation:
(1920 - x)/x * 100 = (x - 1280)/x * 100
Simplifying this equation, we get:
1920 - x = x - 1280
Rearranging the equation, we get:
2x = 3200
x = 1600
To make a 25% profit, the selling price should be 1600 + (0.25 * 1600) = 2000.
Therefore, the article should be sold for Rs. 2000 to make a 25% profit.
45.
On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
Correct Answer
D. Rs 60
Explanation
If the loss on selling 17 balls is equal to the cost price of 5 balls, then the loss on each ball is equal to the cost price of 5/17 balls. Therefore, the selling price of each ball is the cost price plus the loss, which is equal to the cost price of 5/17 balls. We are given that the selling price of 17 balls is Rs. 720, so the selling price of each ball is Rs. 720/17. Equating this to the cost price plus the loss, we get the equation: Rs. 720/17 = cost price + cost price of 5/17 balls. Simplifying this equation, we find that the cost price of each ball is Rs. 60.
46.
A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
Correct Answer
B. 4.14 kmph
Explanation
To find the speed of B, we need to calculate the time taken by both A and B to complete the race.
Since A runs at 5 kmph, it means A covers 5 meters in 1 second.
A gives B a start of 8 meters and still beats him by 8 seconds.
So, A covers 100 meters in (100/5) = 20 seconds.
B takes 8 seconds more than A, so B takes (20 + 8) = 28 seconds to complete the race.
To find the speed of B, we divide the distance (100 meters) by the time taken (28 seconds) and convert it to kmph.
Therefore, the speed of B is 3.57 kmph.
47.
In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
Correct Answer
A. 20 m
Explanation
In a 100 m race, A covers the distance in 36 seconds and B in 45 seconds. To find out how much A beats B by, we need to calculate the difference in their distances covered. A covers 100 m in 36 seconds, which means A covers 100/36 = 2.78 m per second. B covers 100 m in 45 seconds, which means B covers 100/45 = 2.22 m per second. The difference in their speeds is 2.78 - 2.22 = 0.56 m per second. A beats B by this much difference in speed for 36 seconds, which is 0.56 * 36 = 20.16 m. Therefore, A beats B by approximately 20 m.
48.
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
Correct Answer
C. 28 m
Explanation
In the given scenario, A can beat B by 25 m and B can beat C by 4 m. Therefore, it can be inferred that A is faster than B and B is faster than C. To find out how much faster A is than C, we can add the difference between A and B (25 m) to the difference between B and C (4 m). Thus, A can beat C by 29 m.
49.
In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
Correct Answer
D. 60 litres
Explanation
To change the ratio of milk and water from 2:1 to 1:2, we need to add an equal amount of water. The initial mixture contains 2 parts milk and 1 part water, so to make it 1 part milk and 2 parts water, we need to add 2 parts water. Since the initial mixture is 60 liters, we need to add 2 parts water, which is 2 * 60 = 120 liters. Therefore, the quantity of water to be further added is 120 liters.
50.
The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Correct Answer
B. 30
Explanation
Let the three numbers be 2x, 3x, and 8x. According to the given ratio, the sum of the three numbers is 2x + 3x + 8x = 13x. It is given that the sum of the three numbers is 98, so 13x = 98. Solving for x, we get x = 98/13 = 7. Therefore, the second number is 3x = 3 * 7 = 21.