1.
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Correct Answer
B. 7.2
Explanation
To find the person's speed in km per hour, we need to convert the distance from meters to kilometers and the time from minutes to hours. There are 1000 meters in 1 kilometer, so the person crossed 0.6 kilometers. There are 60 minutes in 1 hour, so the person took 1/12 of an hour to cross the street. Dividing the distance by the time, we get a speed of 0.6 / (1/12) = 7.2 km per hour.
2.
An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
Correct Answer
D. 720 kmph
Explanation
To find the speed needed to cover the distance in 1 2/3 hours, we can use the formula speed = distance/time. The distance covered is the same, so we can assume it to be a constant value. The given time is 1 2/3 hours, which can be converted to 5/3 hours. Plugging these values into the formula, we get speed = distance/(5/3) = (3/5) * distance. Since the speed is directly proportional to the distance, we can conclude that the speed needed to cover the distance in 1 2/3 hours is (3/5) times the original speed. Therefore, the correct answer is 720 kmph.
3.
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
Correct Answer
A. 50
Explanation
If a person walks at a speed of 14 km/hr instead of 10 km/hr, the difference in speed is 4 km/hr. It is given that this difference in speed allows the person to walk 20 km more. Therefore, the person would have walked 20 km in 4 hours (20 km / 4 km/hr = 4 hours). Since the person walks at a speed of 10 km/hr, the actual distance traveled by him would be 4 hours multiplied by 10 km/hr, which is equal to 40 km.
4.
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Correct Answer
C. 120 kmph
Explanation
The train and the car both start at the same time and reach point B at the same time, which means they travel the same amount of time. However, the train loses 12.5 minutes while stopping at the stations. This means that the train's travel time is longer than the car's travel time. Since the train travels 50% faster than the car, the car's speed must be 50% of the train's speed. Therefore, if we let the car's speed be x kmph, the train's speed is 1.5x kmph. Since the train and the car travel the same distance, we can set up the equation: (1.5x * travel time) = (x * travel time) + 12.5 minutes. Simplifying this equation, we get x = 120 kmph.
5.
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Correct Answer
B. 10
Explanation
The speed of the bus without stoppages is given as 54 kmph, and with stoppages, it is 45 kmph. The difference in speed is due to the time the bus spends at stoppages. To find the time spent at stoppages per hour, we subtract the speed with stoppages from the speed without stoppages, which gives us 9 kmph. Since 1 kmph is equal to 60 minutes per hour, 9 kmph is equal to 9 * 60 = 540 minutes per hour. Therefore, the bus stops for 540 minutes per hour, which is equivalent to 10 minutes per hour.
6.
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Correct Answer
C. 16
Explanation
A can do 1/20th of the work in a day, B can do 1/30th of the work in a day, and C can do 1/60th of the work in a day. On every third day, A is assisted by B and C, so the combined work done on those days is 1/30 + 1/60 = 1/20th of the work. This means that on every third day, A completes 1/20th of the work. Therefore, in 15 days (5 sets of 3 days), A can complete 5/20th of the work. Adding this to the work A does on the 16th day, A can complete the entire work in 16 days.
7.
A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Correct Answer
A. Rs. 7500
Explanation
B's share in the total profit can be calculated by considering the ratio of their investments and the time period. A and B invested a total of Rs. 35,000 for 2 years, while C joined after 6 months with Rs. 20,000. Therefore, C's investment is equivalent to Rs. 10,000 for 2 years. The total investment for 2 years is Rs. 45,000. B's share can be calculated by finding the ratio of B's investment to the total investment and then multiplying it by the total profit. B's investment is Rs. 15,000, which is 1/3 of the total investment. Thus, B's share in the total profit of Rs. 25,000 is Rs. 7500.
8.
The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:
Correct Answer
B. 108
Explanation
The true discount on a bill is the difference between the face value of the bill and the amount paid. In this case, the true discount is Rs. 90. The banker's discount is always greater than or equal to the true discount. Since the banker's discount is given as one of the answer choices, we can conclude that the correct answer is 108, which is greater than the true discount of Rs. 90.
9.
Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?
Correct Answer
A. Rs. 4000
Explanation
Let the amount invested in the 12% stock at Rs. 120 be x. The amount invested in the 15% stock at Rs. 125 will be (12000 - x).
The dividend earned from the 12% stock at Rs. 120 will be (x/120) * 12 = x/10.
The dividend earned from the 15% stock at Rs. 125 will be ((12000 - x)/125) * 15 = (2400 - 3x)/5.
Given that the total dividend per annum is Rs. 1360, we can set up the equation:
x/10 + (2400 - 3x)/5 = 1360.
Simplifying this equation, we get 5x + 2400 - 3x = 6800.
Solving for x, we find x = 4000.
Therefore, Sakshi invests Rs. 4000 in the 12% stock at Rs. 120.
10.
If 5a = 3125, then the value of 5(a - 3) is:
Correct Answer
A. 25
Explanation
To find the value of 5(a - 3), we can substitute the given value of 5a = 3125 into the expression. By substituting, we get 5(3125/5 - 3), which simplifies to 5(625 - 3). Further simplifying, we have 5(622), which equals 3110. Therefore, the correct answer is 25.
11.
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Correct Answer
C. 44%
Explanation
When each side of a rectangle is increased by 20%, the area of the rectangle will also increase. To find the percentage increase in the area, we can use the formula: (new area - original area) / original area * 100. Since the sides are increased by 20%, the new length and width will be 120% of the original length and width. Therefore, the new area will be (1.2 * original length) * (1.2 * original width) = 1.44 * original area. The percentage increase in the area is then (1.44 - 1) / 1 * 100 = 44%.
12.
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
Correct Answer
A. 1
Explanation
Due to bad weather, the aircraft's average speed for the trip was reduced by 200 km/hr. This reduction in speed caused the flight to take longer, resulting in an increase in the time of flight by 30 minutes. Since the distance of the flight remains the same at 600 km, the duration of the flight can be calculated by dividing the distance by the average speed. As the speed was reduced by 200 km/hr, the duration of the flight will be longer than if the speed remained constant. Therefore, the correct answer is 1, indicating that the duration of the flight is longer than initially planned.
13.
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
Correct Answer
A. 625
Explanation
Let's assume the principal amount is x. The formula for calculating compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the interest is compounded annually, so n = 1.
Given that the difference between the compound interest and simple interest is Re. 1, we can set up the equation:
A - P = 1
Using the formula for compound interest, we can calculate the compound interest for 2 years at 4% per annum:
A = x(1 + 0.04)^2
Substituting the values into the equation:
x(1 + 0.04)^2 - x = 1
Simplifying the equation:
1.0816x - x = 1
0.0816x = 1
x = 1 / 0.0816
x ≈ 12.25
Therefore, the sum of money is approximately Rs. 625.
14.
The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Correct Answer
B. 500
Explanation
Let the principal amount be P. The compound interest formula is given by A = P(1 + r/n)^(nt), where A is the final amount, r is the rate of interest, n is the number of times interest is compounded in a year, and t is the time in years. From the given information, we can calculate that P(1 + 0.1/1)^(1*2) = P(1.1)^2 = P * 1.21 = P + 525. Solving this equation, we find that P = Rs. 1000. The simple interest formula is given by SI = (P * r * t) / 100. Plugging in the values, we get SI = (1000 * 5 * 4) / 100 = Rs. 500. Therefore, the answer is 500.
15.
A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
Correct Answer
C. 25 : 18
Explanation
When a cube is formed by melting three smaller cubes, the volume of the large cube is equal to the sum of the volumes of the smaller cubes. In this case, the volume of the large cube is 3^3 + 4^3 + 5^3 = 216 cm^3.
The surface area of a cube is given by 6a^2, where a is the length of one side. Therefore, the total surface area of the three smaller cubes is 6(3^2) + 6(4^2) + 6(5^2) = 6(9 + 16 + 25) = 6(50) = 300 cm^2.
The surface area of the large cube is 6(6^2) = 6(36) = 216 cm^2.
The ratio of the total surface areas of the smaller cubes to the large cube is 300:216, which simplifies to 25:18.
16.
66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
Correct Answer
A. 84
Explanation
When a wire is drawn from a material, its volume remains constant. The volume of the wire can be calculated using the formula V = πr²h, where r is the radius and h is the height. In this case, the radius is given as 0.5 mm (since the diameter is 1 mm) and the volume is given as 66 cubic centimeters. By rearranging the formula, we can solve for the height (length) of the wire: h = V / (πr²). Plugging in the values, we get h = 66 / (π * (0.5²)). Simplifying this equation, we find that the length of the wire is approximately 84 meters.
17.
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
In this question, we are given a number with 3 digits whose sum is 10. Let's assume the number is ABC, where A, B, and C are the digits. We are also given that the middle digit is equal to the sum of the other two digits. So, B = A + C. Additionally, if we reverse the digits of the number, it increases by 99. This means that if we reverse ABC, we get CBA and CBA - ABC = 99. From these conditions, we can deduce that A = 2, B = 5, and C = 3. Therefore, the number is 253.
18.
How many times in a day, the hands of a clock are straight?
Correct Answer
C. 44
Explanation
The hands of a clock are straight twice in a day, once at 12 o'clock and once at 6 o'clock. However, each time the hands are straight, they are straight for two minutes. Therefore, in a day, the hands of a clock are straight a total of 44 times (2 minutes x 22 times).
19.
Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Correct Answer
A. 20
Explanation
Since pipe A can fill the tank in 36 hours and pipe B can fill the tank in 45 hours, it means that in 1 hour pipe A can fill 1/36 of the tank and pipe B can fill 1/45 of the tank. When both pipes are opened simultaneously, they will fill the tank at a combined rate of (1/36) + (1/45) = 5/180 + 4/180 = 9/180 = 1/20 of the tank per hour. Therefore, it will take 20 hours to fill the tank when both pipes are opened simultaneously.
20.
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
Correct Answer
D. 10
Explanation
Let's assume C's age to be x. According to the given information, B's age is twice that of C, so B's age is 2x. A is two years older than B, so A's age is 2x + 2. The total of their ages is 27, so x + 2x + 2 + 2x = 27. Simplifying the equation, we get 5x + 2 = 27. Solving for x, we find that x = 5. Therefore, B's age is 2x = 2 * 5 = 10.