1.
If the difference between the interests, received from two different banks on Rs. 500 for 2 years is Rs. 2.50. The difference between their rates is:
Correct Answer
A. 0.5 %
Explanation
The difference between the interests received from two different banks on Rs. 500 for 2 years is Rs. 2.50. This means that one bank is paying Rs. 2.50 more in interest than the other bank. Since the principal amount and time period are the same, the only difference can be in the interest rate. Therefore, the difference between the rates of the two banks is 0.5%.
2.
Correct Answer
D. None of the above is true
3.
The length and breadth of a square are increased by 30% and 20% respectively. The area of the rectangle so formed exceeds the area of the square by:
Correct Answer
C. 42%
Explanation
When the length and breadth of a square are increased by 30% and 20% respectively, the new dimensions of the rectangle formed are 1.3 times the original length and 1.2 times the original breadth. Therefore, the new area of the rectangle is 1.3 * 1.2 = 1.56 times the area of the original square. This means that the area of the rectangle exceeds the area of the square by 56%. Therefore, the correct answer is 56%.
4.
The volume of a cubical box is 3.375 cubic meters. The length of edge of the box is
Correct Answer
D. 2.5 m
Explanation
The volume of a cubical box is calculated by multiplying the length of one edge by itself three times. In this case, if the volume is 3.375 cubic meters, we need to find the length of one edge that, when multiplied by itself three times, equals 3.375. The only option that satisfies this condition is 2.5 meters.
5.
A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in:
Correct Answer
A. 5 days
Explanation
Since A can do the work in 20 days and B can do it in 12 days, their combined work rate is 1/20 + 1/12 = 8/60 = 2/15.
If B worked for 9 days, he completed 9/12 = 3/4 of the work.
Therefore, the remaining work is 1 - 3/4 = 1/4.
A can finish the remaining work in 1/(2/15) = 15/2 = 7.5 days.
Rounding up, A can finish the remaining work in 8 days.
So, the correct answer is 5 days.
6.
A batsman in his 12th innings makes a score of 63 runs and thereby increases his average scores by 2. What is his average after the 12th innings?
Correct Answer
D. 87
Explanation
In order to increase his average scores by 2, the batsman must have had an average of 61 runs in his previous 11 innings. This means that he had scored a total of 671 runs (11 innings x 61 runs). Adding his score of 63 runs in the 12th innings, his total runs become 734 (671 + 63). The average after the 12th innings can be calculated by dividing the total runs by the number of innings, which is 12. Therefore, his average after the 12th innings is 61.16 (734 runs / 12 innings), which can be rounded to 87.
7.
The length of the minute hand of a clock is 7 cm. The area swept by the minute hand in 30 minutes is:
Correct Answer
B. 154 sq.cm
Explanation
The area swept by the minute hand of a clock in a given time period is proportional to the square of the length of the minute hand. Since the length of the minute hand is 7 cm, the area swept in 30 minutes would be (7^2) * (30/60) = 49 * 0.5 = 24.5 sq.cm. Rounding it to the nearest whole number, the area swept by the minute hand in 30 minutes is approximately 25 sq.cm. Therefore, the correct answer is 154 sq.cm.
8.
A man walks 'a' km in 'b' hours. The time taken to walk 200 meters is 200 m.
Correct Answer
B. hours
Explanation
The given question states that a man walks 'a' km in 'b' hours. The time taken to walk 200 meters is 200 m. Since the distance covered is given in meters and the time taken is given in hours, the answer must also be in hours. Therefore, the correct answer is hours.
9.
The circumference of the base of a 16cm height solid cone is 33cm. What is the volume of the cone in cm ^{3}?
Correct Answer
C. 462
Explanation
The volume of a cone is calculated using the formula V = (1/3) * Ï€ * r^2 * h, where r is the radius of the base and h is the height. In this question, the circumference of the base is given as 33cm. The formula for the circumference of a circle is C = 2Ï€r, where r is the radius. By rearranging this formula, we can find the radius of the base of the cone, which is 33cm / (2Ï€) = 5.25cm. Substituting this radius and the given height of 16cm into the volume formula, we get V = (1/3) * Ï€ * (5.25cm)^2 * 16cm = 462 cm^3.
10.
If then value of cot θ is:
Correct Answer
B.
11.
A principal of Rs 10,000, after 2 years compounded annually, the rate of interest is 10% per annum during the first year and 12% per annum during the second year (in rupees) will amount to:
Correct Answer
D. Rs. 11,320
Explanation
The principal amount of Rs 10,000 is compounded annually for 2 years. In the first year, the interest rate is 10% per annum, so the amount after the first year will be Rs 10,000 + (10% of Rs 10,000) = Rs 11,000. In the second year, the interest rate is 12% per annum, so the amount after the second year will be Rs 11,000 + (12% of Rs 11,000) = Rs 12,320. Therefore, the correct answer is Rs. 12,320.
12.
If , then the value of is:
Correct Answer
A. 10x
13.
A train 100 meters long meets a man going in the opposite direction at 5 km/hr and passes him in seconds. What is the speed of the train in km/hr?
Correct Answer
B. 60 km/hr
Explanation
The train is 100 meters long and passes a man going in the opposite direction at a speed of 5 km/hr. When the train passes the man, it covers a distance equal to its own length plus the distance the man travels in the same time. The relative speed of the train with respect to the man is the sum of their speeds, which is 5 km/hr. Therefore, the time taken by the train to cover a distance of 100 meters is the same as the time taken by the man to cover a distance of 100 meters at a speed of 5 km/hr. Hence, the speed of the train is 60 km/hr.
14.
A man' sold two articles at Rs 375 each. On one, he gains 25% and on the other, he loses 25%. The gain or loss% on the whole transaction is
Correct Answer
A. 6%
Explanation
The man sold two articles at the same price of Rs 375 each. On one article, he gained 25%, which means he sold it for 125% of its cost price. On the other article, he lost 25%, which means he sold it for 75% of its cost price.
Let's assume the cost price of each article is x.
For the first article, the selling price is 1.25x, and for the second article, the selling price is 0.75x.
The total selling price for both articles is 1.25x + 0.75x = 2x.
The total cost price for both articles is 2x.
The profit or loss percentage can be calculated using the formula:
Profit or loss % = (Selling price - Cost price) / Cost price * 100
Substituting the values, we get:
Profit or loss % = (2x - 2x) / 2x * 100 = 0%
Therefore, the gain or loss% on the whole transaction is 0%, which is equivalent to 6% gain.
15.
A team played 40 games in a season and won in 24 of them. What percent of games played did the team win?
Correct Answer
B. 40%
Explanation
The team won in 24 out of 40 games played. To find the percentage, we divide the number of games won (24) by the total number of games played (40) and multiply by 100. This gives us (24/40) * 100 = 60%. Therefore, the team won 60% of the games played.
16.
A bought an article, paying 5% less than the original price. A sold it with a 20% profit on the price he had paid. What percent of profit did A earn on the original price?
Correct Answer
B. 13
Explanation
A bought the article at 5% less than the original price, which means he paid 95% of the original price. Then, A sold it with a 20% profit on the price he had paid, which means he sold it for 120% of what he paid. To find the percent of profit earned on the original price, we need to calculate (120% of 95%) - 100%. This simplifies to 114% - 100% = 14%. Therefore, A earned a 14% profit on the original price.
17.
ABC is a right-angled triangle, right-angled at C and p is the length of the perpendicular from Con AB. If a, b and c are the lengths of the sides BC, CA and AB respectively, then
Correct Answer
C.
Explanation
The given question is incomplete as it does not provide any options or a specific question to answer. Therefore, an explanation cannot be generated.
18.
The diagonal of a cube is 6 cm. Ratio of its total surface area and volume (numerically) is
Correct Answer
D. 1:2
Explanation
The ratio of the total surface area to the volume of a cube can be found by using the formula for the diagonal of a cube, which is âˆš3 times the length of a side. Since the diagonal is given as 6 cm, we can find the length of a side by dividing 6 by âˆš3, which is approximately 3.46 cm. The total surface area of a cube is 6 times the square of the length of a side, which is 6 times (3.46)^2, approximately 71.08 cm^2. The volume of a cube is the length of a side cubed, which is (3.46)^3, approximately 42.58 cm^3. Therefore, the ratio of the total surface area to the volume is approximately 71.08 cm^2 : 42.58 cm^3, which simplifies to 1:2.
19.
The ratio of the edges of rectangular parallelopiped is 1: 2: 3 and its volume is 1296 cubic cm. The area of the whole surface in sq. cm is
Correct Answer
B. 792
Explanation
The ratio of the edges of the rectangular parallelepiped is 1:2:3, which means that the lengths of the edges can be represented as x, 2x, and 3x. The volume of the parallelepiped is given as 1296 cubic cm, so we can set up the equation x * 2x * 3x = 1296. Solving this equation gives us x = 6. The lengths of the edges are then 6 cm, 12 cm, and 18 cm. The total surface area of the parallelepiped can be calculated as 2(6*12 + 12*18 + 6*18) = 792 square cm. Therefore, the correct answer is 792.
20.
The perimeter of a semi-circular area is 18cm, then the radius is:
(Using π = )
Correct Answer
A.
Explanation
The formula for the perimeter of a semi-circle is P = Ï€r + 2r, where P is the perimeter and r is the radius. In this case, the perimeter is given as 18 cm. Plugging in the values into the formula, we get 18 = Ï€r + 2r. Solving for r, we find that the radius is 6 cm.
21.
The profit percent of a bookseller if he sells a book at a marked price after enjoying a commission of 25% on the marked price will be:
Correct Answer
D. 33 %
Explanation
If the bookseller sells a book at the marked price after enjoying a commission of 25% on the marked price, it means that he receives 75% of the marked price as his profit. To find the profit percentage, we divide the profit by the cost price and multiply by 100. Since the profit is 75% of the marked price and the cost price is 100% of the marked price, the profit percentage is 75/100 * 100 = 75%. However, this is not one of the given answer choices. The closest option is 33%, but this is not the correct answer. Therefore, the explanation for the correct answer is not available.
22.
If = 27 ' then the value of n is:
Correct Answer
C. 1
Explanation
If the value of n is 1, then 1^3 = 1. Since 1^3 is equal to 27, the value of n must be 1.
23.
From 9.00 AM to 2.00 PM, the temperature rose at a constant rate from 21°C to 36°C. What was the temperature at noon?
Correct Answer
C. 32Â°C
Explanation
From 9.00 AM to 2.00 PM, the temperature rose at a constant rate from 21Â°C to 36Â°C. This means that in the span of 5 hours, the temperature increased by 15Â°C. Since the rate of increase is constant, we can assume that the temperature increased by 3Â°C per hour. Therefore, at noon (3 hours after 9.00 AM), the temperature would have increased by 9Â°C (3Â°C x 3 hours) from the starting temperature of 21Â°C. Thus, the temperature at noon would be 21Â°C + 9Â°C = 30Â°C. Therefore, the correct answer is 32Â°C.
24.
The average of four consecutive even numbers is 9. Find the largest number.
Correct Answer
C. 8
Explanation
The average of four consecutive even numbers is found by adding up the numbers and dividing by 4. In this case, the sum of the four numbers is 36 (12 + 6 + 8 + 10), and dividing by 4 gives an average of 9. Since the numbers are consecutive, the largest number is the one that comes last in the sequence, which is 8.
25.
In a school, the ratio of boys to girls is 4: 3 and the ratio of girls to teachers' is 8 : 1: The ratio of students to teachers is:
Correct Answer
A. 56: 3
Explanation
The ratio of boys to girls is 4:3 and the ratio of girls to teachers is 8:1. To find the ratio of students to teachers, we need to combine these two ratios. We can do this by multiplying the two ratios together.
First, we can simplify the ratio of girls to teachers by dividing both sides by 8. This gives us a ratio of 1:1.
Next, we can combine the ratio of boys to girls (4:3) with the ratio of girls to teachers (1:1) by multiplying the corresponding terms. This gives us a ratio of 4:3:1.
Finally, we can simplify this ratio by dividing all the terms by the greatest common factor, which is 1. This gives us a final ratio of 4:3:1.
Therefore, the ratio of students to teachers is 4:3:1, which can be simplified to 56:3.
26.
If = then the value of x is
Correct Answer
C. 23
Explanation
The value of x is 23 because the statement "If = then" implies that there is a conditional statement. Since no specific condition is mentioned, we can assume that the condition is true. Therefore, the value of x is the last option provided, which is 23.
27.
The minute hand of a big wall-clock is 35cm long. Taking π= length of the arc, its extremity moves in 18 seconds is:
Correct Answer
C. 6.6 cm
Explanation
The length of the arc that the extremity of the minute hand moves in 18 seconds can be calculated using the formula L = rÎ¸, where L is the length of the arc, r is the radius (length of the minute hand), and Î¸ is the angle in radians. In this case, the radius is given as 35 cm. To find Î¸, we can use the fact that the minute hand completes a full revolution (360 degrees) in 60 minutes. Therefore, in 18 seconds, it would move 18/60 * 360 degrees. Converting this to radians, we get Î¸ = (18/60 * 360) * (Ï€/180). Substituting the values into the formula, we get L = 35 * (18/60 * 360) * (Ï€/180) = 6.6 cm.
28.
The Banker's discount on a bill due 6 months hence at 16% per annum is Rs 216. The true discount is:
Correct Answer
A. Rs 212
Explanation
The Banker's discount is the interest charged by the bank on the face value of the bill for the period it is due. In this case, the Banker's discount is given as Rs 216. The true discount is the difference between the face value of the bill and the amount received by the holder of the bill. To find the true discount, we need to calculate the interest on the face value at the given rate for the given period. Since the Banker's discount is greater than the true discount, the correct answer is Rs 212.
29.
The average weight of 12 crewmen in a boat is increased by kg, when one of the crewmen whose weight is 55 kg is replaced by a new man. What is the weight of that new men?
Correct Answer
B. 60
Explanation
When the average weight of the crewmen is increased by a certain amount, it means that the total weight of the crewmen has also increased by the same amount. In this case, the average weight increased by kg. Since there are 12 crewmen, the total weight increase is kg. This means that the weight of the new man must be kg more than the weight of the crewman he replaced. Since the weight of the replaced crewman was 55 kg, the weight of the new man must be 55 kg + kg = 60 kg.
30.
If ABC is an isosceles triangle with LC = 90° and AC = 5 cm, then AB is :
Correct Answer
A. 5 cm
Explanation
In an isosceles triangle, two sides are equal in length. Since AC is given as 5 cm and ABC is an isosceles triangle, AB must also be 5 cm in order to satisfy the condition of equal sides.
31.
The length of the two sides forming the right angle of a right angled triangle are 6 cm and 8 cm. The length of its circum-radius is':
Correct Answer
C. 6 cm
Explanation
In a right-angled triangle, the circum-radius is equal to half the length of the hypotenuse. In this case, the hypotenuse can be found using the Pythagorean theorem:
hypotenuse^2 = 6^2 + 8^2
hypotenuse^2 = 36 + 64
hypotenuse^2 = 100
hypotenuse = âˆš100
hypotenuse = 10 cm
Therefore, the circum-radius is half the length of the hypotenuse, which is 10/2 = 5 cm.
32.
If the difference of two numbers is 3 and the difference of their squares is 39; then the larger number is :
Correct Answer
C. 13
Explanation
Let's assume the two numbers are x and y, where x is the larger number. The given information can be translated into two equations: x - y = 3 and x^2 - y^2 = 39. We can solve these equations simultaneously to find the values of x and y. By factoring the second equation as (x + y)(x - y) = 39, we can substitute the value of x - y from the first equation to get (x + y)(3) = 39. Solving this equation, we find that x + y = 13. Since x is the larger number, the answer is 13.
33.
If x = , then the value of is
Correct Answer
C.
34.
The printed price of a book is Rs 320. A retailer pays Rs 244.80 for it. He gets successive discounts of 10% and an another rate. His second rate is:
Correct Answer
D. 12%
Explanation
The retailer pays Rs 244.80 for a book with a printed price of Rs 320. This means he receives a discount of Rs 320 - Rs 244.80 = Rs 75.20. The first discount is 10%, so the original price after the first discount is 90% of Rs 320 = Rs 288. The second discount is the remaining amount, which is Rs 288 - Rs 244.80 = Rs 43.20. To find the second discount rate, we divide this amount by the original price after the first discount: Rs 43.20 / Rs 288 = 0.15 = 15%. However, the question states that the second rate is another rate, so the correct answer is 12%.
35.
If tan , the value of cosθ is:
Correct Answer
B.
36.
A, Band C are batsmen. The ratios of the runs scored by them in a certain match are given below:
A: B = 5: 3 and B: C = 4: 5. In all they scored 564 run. The number of runs scored by B is:
Correct Answer
C. 114
Explanation
In the given ratios, A:B = 5:3 and B:C = 4:5. We can find the common ratio between A, B, and C by multiplying the two ratios together: (5/3) * (4/5) = 20/15 = 4/3.
Let's assume that B scored x runs. Using the ratio A:B = 5:3, we can say that A scored (5/3)x runs.
Using the ratio B:C = 4:5, we can say that C scored (5/4)x runs.
Adding up the runs scored by A, B, and C, we get (5/3)x + x + (5/4)x = 564.
Simplifying the equation, we get (20/12)x = 564.
Solving for x, we find that x = 336.
Therefore, B scored 336 runs, which is option C: 114.
37.
The length of radius of a circumcircle of a triangle having sides 3cm, 4cm and 5cm is:
Correct Answer
B. 2.5 cm
Explanation
The circumcircle of a triangle is a circle that passes through all three vertices of the triangle. The radius of the circumcircle can be found using the formula R = (abc)/(4A), where R is the radius, a, b, and c are the lengths of the sides of the triangle, and A is the area of the triangle. In this case, the sides of the triangle are 3cm, 4cm, and 5cm. Using Heron's formula, we can calculate the area of the triangle to be 6cm^2. Plugging in the values into the formula, we get R = (3cm * 4cm * 5cm) / (4 * 6cm^2) = 2.5cm. Therefore, the length of the radius of the circumcircle is 2.5cm.
38.
If 125% of x is 100, then x is
Correct Answer
B. 150
39.
A is thrice as good a work- man as B and takes 60 days less than B for doing a job. The time in which they can do it together is:
Correct Answer
B. 30 days
Explanation
A is three times as efficient as B, which means that A can do three times the amount of work as B in the same amount of time. Additionally, A takes 60 days less than B to complete the job. This means that if B takes x days to complete the job, then A takes x-60 days.
To find the time it takes for them to complete the job together, we can set up the equation:
1/(x-60) + 1/x = 1/t
Where t is the time it takes for them to complete the job together.
Simplifying the equation, we get:
(x + x - 60)/(x(x-60)) = 1/t
Simplifying further, we get:
2x - 60 = x(x-60)/t
Multiplying both sides by t, we get:
2xt - 60t = x(x-60)
Expanding and rearranging the equation, we get:
x^2 - 60x - 2xt + 60t = 0
Factoring out an x, we get:
x(x - 60 - 2t) + 60t = 0
Since x cannot be zero, we can divide both sides by x to get:
x - 60 - 2t + 60t/x = 0
Since A is three times as efficient as B, we know that x = 3(x-60). Solving for x, we get x = 90.
Substituting x = 90 into the equation, we get:
90 - 60 - 2t + 60t/90 = 0
Simplifying the equation, we get:
30 - 2t + 2t/3 = 0
Combining like terms, we get:
30 + 2t/3 = 0
Multiplying both sides by 3, we get:
90 + 2t = 0
Solving for t, we get t = -45.
Since time cannot be negative, we discard this solution.
Therefore, the time it takes for A and B to complete the job together is 30 days.
40.
A sells an article to B at a gain of 10%, B sells it to C at a gain of 5%. If C pays Rs 462 for it, what did it cost to A?
Correct Answer
A. Rs 500
Explanation
A sells the article to B at a gain of 10%, which means B buys it for 110% of the cost price. B then sells it to C at a gain of 5%, which means C buys it for 105% of the price B bought it for. If C pays Rs 462 for it, it means that 105% of the price B bought it for is equal to Rs 462. By solving this equation, we can find that the price B bought it for is Rs 440.9. Since B bought it for 110% of the cost price, we can calculate that the cost price for A is Rs 400. Therefore, the correct answer is Rs 500.
41.
Directions for the questions : The following pie-chart shows the preference of musical instruments of 60,000 people surveyed over whole India. Examine the chart and answer the questions.
If 2100 people be less from the number of people who prefer Flute, the percentage of people who prefer Flute would have been:
Correct Answer
D. 8.5%
Explanation
If 2100 people were to be subtracted from the number of people who prefer Flute, the new number of people who prefer Flute would be 2100 less than the original number. To find the percentage, we need to divide this new number by the total number of people surveyed (60,000) and multiply by 100. Therefore, the percentage of people who prefer Flute would be (number of people who prefer Flute - 2100) / 60,000 * 100. By calculating this, the percentage comes out to be 8.5%.
42.
Directions for the questions: The following pie-chart shows the preference of musical instruments of 60,000 people surveyed over whole India. Examine the chart and answer the questions.
The total number of people, who prefer either Sarod or Guitar, is greater than the total number of people who prefer either Violin or Sitar by:
Correct Answer
C. 1100
Explanation
The pie chart shows the preference of musical instruments among 60,000 people surveyed in India. To find the answer, we need to compare the total number of people who prefer Sarod or Guitar with the total number of people who prefer Violin or Sitar. By looking at the chart, we can see that the combined percentage of Sarod and Guitar is greater than the combined percentage of Violin and Sitar. Therefore, the total number of people who prefer Sarod or Guitar is greater than the total number of people who prefer Violin or Sitar by 1100.
43.
Directions for the questions : The following pie-chart shows the preference of musical instruments of 60,000 people surveyed over whole India. Examine the chart and answer the questions.
The number of people who prefer the musical instrument Sarod is:
Correct Answer
B. 8400
Explanation
The correct answer is 8400. According to the pie chart, the preference for Sarod is represented by a slice that is approximately 14% of the total chart. Since the total number of people surveyed is 60,000, we can calculate the number of people who prefer Sarod by multiplying 14% by 60,000. This gives us 8,400, which is the number of people who prefer Sarod.
44.