1. If pipe A can fill the tank in 45 minutes and pipe B in 30 minutes, find the time to fill the tank if both the pipes are opened together.

A. 12 minutes B. 20 minutes C. 18 minutes D. 15 minutes

Answer: Option C
Explanation: In 1 minute pipe A can fill [latex]\frac{1}{45 }[/latex]th part of the tank and pipe B can fill [latex]\frac{1}{30 }[/latex]th part of the tank. If they are opened simultaneously then in 1 minute they can fill ([latex]\frac{1}{45 }[/latex] + [latex]\frac{1}{30 }[/latex]) part of the tank = [latex]\frac{1}{18 }[/latex]th part of the tank. Hence, in 18 minutes the tank gets filled if pipes A & B are opened together.
2. Find the ratio in which wheat of inferior quality (Rs.14/kg) be mixed with the wheat of superior quality (Rs.28/kg) so that the shopkeeper gains Rs.2 by selling the resulting mixture at Rs.20/kg.

A. 1 : 3 B. 5 : 2 C. 3 : 4 D. 2 : 5

Answer: Option B
Explanation: Let the resulting mixture be 1 kg, and x kg be the amount of wheat of inferior quality. Therefore, (1-x)kg is the amount of wheat of superior quality. As the shopkeeper gains Rs.2, the cost of the mixture is Rs.18 14*x + 28*(1-x) = 18 14x - 28x + 28 = 18 14x = 10 x = [latex]\frac{5}{7}[/latex] (1 – x) = [latex]\frac{2}{7 }[/latex] x : (1-x) = [latex]\frac{5}{7 }[/latex] : [latex]\frac{2}{7 }[/latex] = 5 : 2
3. Find the area of the square field if a train 800 meters long passes the field with a speed of 120 kmph in one minute.

A. 1.44 sq. km B. 4 sq. km C. 2 sq. km D. 2.64 sq. km

Answer: Option A
Explanation: 120 km/hr = 120 * [latex]\frac{5}{18 }[/latex] = 33.33 m/s v = [latex]\frac{d}{t }[/latex] ; 33.33 = [latex]\frac{d}{60 }[/latex] d = 2000 m Hence, in one minute the train travels 2000 m. But, as the train is 800 m long and it passes the field, the length of the field is 2000 – 800 = 1200 m. Area = 1200 * 1200 = 1.44 sq. km Therefore, It takes B [latex]\frac{8}{3}[/latex] hours to catch up with A. Distance: [latex]\frac{8}{3}[/latex] x 10 = [latex]\frac{8}{3}[/latex] km = 26.67
4. If the ratio of present ages of Jeet and Jay is 5:7 and after 6 years the ratio will be 3:4, what is the present age of Jay?

A. 42 B. 30 C. 36 D. None of these

Answer: Option A
Explanation: As the present age of Jeet and Jay are in the ratio 5:7, let their ages be 5x and 7x respectively. Therefore, their ages after 6 years will be (5x+6) and (7x+6) respectively. Now, it is given that [latex]\frac{(5x+6)}{(7x+6)}[/latex] = [latex]\frac{3}{4}[/latex] 4*(5x+6) = 3*(7x+6) x = 6 Hence, the present age of Jay is 7x = 7*6 = 42 years
5. A military camp has a food reserve for 250 personnel for 40 days. If after 15 days 50 more personnel are added to the camp, find the number of days the reserve will last for?

A. 20 B. 36 C. 25 D. 42

Answer: Option C
Explanation: As the camp has a reserve for 250 personnel that can last for 40 days, after 10 days the reserve left for 250 personnel is for 30 days. Now 50 more personnel are added in the camp. Hence, the food reserve for 300 personnel will last for: 250:300::x:30 ……..(it is an indirect proportion as less men means more days) x = [latex]\frac{(250*30)}{300}[/latex] x = 25 days

1. Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?

A. [latex]\frac{8}{35}[/latex] B. [latex]\frac{34}{35}[/latex] C. [latex]\frac{27}{35}[/latex] D. None of these

Answer: Option A
Explanation: P(A) = 2/5 P(B) = 4/7 E = {A and B both get selected} P(E) = P(A)*P(B) = [latex]\frac{2}{5}[/latex] * [latex]\frac{4}{7}[/latex] = [latex]\frac{8}{35}[/latex]
2. Find the number of shares that can be bought for Rs.8200 if the market value is Rs.20 each with brokerage being 2.5%.

A. 450 B. 500 C. 400 D. 410

Answer: Option C
Explanation: Cost of each share = (20 + 2.5% of 20) = Rs.20.5 Therefore, number of shares = [latex]\frac{8200}{20.5}[/latex] = 400
3. The ratio of the current ages of Ajay and Vijay is 7:4. The ratio between Ajay’s age 6 years ago and Vijay’s age 6 years from now is 1:1. Find the ratio between Ajay’s age 12 years hence and Vijay’s age 12 years ago.

A. 12:1 B. 10:1 C. 1:1 D. None of these

Answer: Option B
Explanation: Let the current age of Ajay and Vijay be 7x and 4x respectively. [latex]\frac{(7x – 6)}{4x + 6 }[/latex] = [latex]\frac{1}{1}[/latex] 7x – 6 = 4x + 6 3x = 12 x = 4 Therefore, [latex]\frac{(7x + 12)}{(4x – 12)}[/latex] = [latex]\frac{(7*4 + 12)}{(4 * 4 -12) }[/latex] = [latex]\frac{40}{4}[/latex] = [latex]\frac{10}{1}[/latex]
4. The ratio of the areas of a square and rhombus whose base is same is:

A. 1:2 B. 2:1 C. 1:1 D. 3:1

Answer: Option C
Explanation: The square and the rhombus are equal in area if they have a common base.
5. If in a race of 80m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:

A. 20m B. 16m C. 11m D. 10m

Answer: Option B
Explanation: The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds. The distance covered by B in 5 seconds = [latex]\frac{(80 * 5)}{25 }[/latex] = 16m Hence, A beats B by 16m.

1. Ravi started off with a business with a capital of Rs.60000. Later he was joined by Kishan with Rs.40000 as his share. If Kishan received 1/3rd of the total profit after 1 year, for how many months did he invest?

A. 8 B. 4 C. 3 D. 9

Answer: Option D
Explanation: Let Ravi’s share be X and Kishan’s share be Y. X : Y = 2 : 1 = 60000*12 : 40000*t ….(where t is number of months Kishan invested his money) 2 : 1 = 72 : 4t 36 = 4t t = 9
2. [latex]\frac{6}{7 }[/latex] of a certain number is 96. Find quarter of that number.

A. 112 B. 32 C. 56 D. 28

Answer: Option D
Explanation: [latex]\frac{6}{7 }[/latex] x = 96 x = 112 y = [latex]\frac{X}{4 }[/latex] = [latex]\frac{112}{4 }[/latex] = 28
3. 3 bells beep at an interval of 12, 20, and 35 minutes. If they beep together at 10 a.m., then they will again beep together at:

A. 12 p.m. B. 1 p.m. C. 4 p.m. D. 5 p.m.

Answer: Option D
Explanation: The L.C.M. of 12, 20 and 35 is 420. Hence, all 3 bells beep together after 420 minutes = 7 hours Hence, the 3 bells will beep together 7 hours after 10 a.m. i.e. at 5 p.m.
4. A scale 6 ft. 8 inches long is divided into 4 equal parts. Find the length of each part.

A. 17 inches B. 20 inches C. 15 inches D. 18 inches

Answer: Option B
Explanation: Total length of scale in inches = (6*12) + 8 = 80 inches Length of each of the 4 parts = [latex]\frac{80}{4 }[/latex] = 20 inches
5. The sum of the two numbers is 73 and their difference is 28. Find the difference between their squares.

101 B. 45 C. 2044 D. cannot be determined

Answer: Option C
Explanation: Let x and y be the two given numbers (x + y) = 73; (x – y) = 28 (x2 – y2) = (x + y) (x – y) = 73*28 = 2044