Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. Three years ago, A was 5 times as old as B. If B is now 8 years old, how old is A now?

A. 28
B. 30
C. 25
D. 20

Solution

Three years ago, B was 5 years old. Therefore, A was 5 * 5 = 25 years old. Now, A is 25 + 3 = 28 years old.

Correct Answer: A — 28

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Q. Three years ago, A was 5 years older than B. If B is now 12 years old, how old is A now?

A. 10
B. 12
C. 15
D. 18

Solution

Three years ago, B was 12 - 3 = 9 years old. A was 9 + 5 = 14 years old now.

Correct Answer: C — 15

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Q. Two coins are tossed. What is the probability of getting at least one head?

A. 1/4
B. 1/2
C. 3/4
D. 1/3

Solution

The possible outcomes are HH, HT, TH, TT. The outcomes with at least one head are HH, HT, TH. So, the probability is 3/4.

Correct Answer: C — 3/4

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Q. Two dice are rolled. What is the probability that the sum of the numbers on the dice is 7?

A. 1/6
B. 1/12
C. 1/36
D. 5/36

Solution

The combinations that give a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). There are 6 combinations out of 36 total outcomes, so the probability is 6/36 = 1/6.

Correct Answer: D — 5/36

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Q. Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 7 hours
B. 8 hours
C. 9 hours
D. 10 hours

Solution

The combined rate is 1/12 + 1/18 = 5/36. Therefore, it will take 36/5 = 7.2 hours to fill the tank.

Correct Answer: C — 9 hours

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Q. Two pipes can fill a tank in 10 hours and 15 hours respectively. How long will it take to fill the tank if both pipes are opened together?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/10 + 1/15 = 3/30 + 2/30 = 5/30. Therefore, it will take 30/5 hours or 6 hours.

Correct Answer: B — 5 hours

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Q. Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 6 hours
B. 7.5 hours
C. 8 hours
D. 9 hours

Solution

The combined rate is 1/10 + 1/15 = 1/6. Therefore, it will take 6 hours to fill the tank.

Correct Answer: B — 7.5 hours

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Q. Two pipes can fill a tank in 10 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank?

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours

Solution

The first pipe fills 1/2 of the tank in 5 hours. The remaining half can be filled by both pipes in 2 hours.

Correct Answer: B — 4 hours

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Q. Two pipes can fill a tank in 18 hours and 24 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 10 hours
B. 12 hours
C. 15 hours
D. 20 hours

Solution

The combined rate is 1/18 + 1/24 = 4/72 + 3/72 = 7/72. Thus, it will take 72/7 hours or approximately 10.29 hours.

Correct Answer: B — 12 hours

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Q. Two pipes can fill a tank in 20 hours and 30 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The combined rate is 1/20 + 1/30 = 3/60 + 2/60 = 5/60. Thus, it will take 60/5 = 12 hours.

Correct Answer: B — 15 hours

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Q. Two pipes can fill a tank in 4 hours and 6 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

The combined rate is 1/4 + 1/6 = 3/12 + 2/12 = 5/12. Therefore, it will take 12/5 hours or 2.4 hours.

Correct Answer: B — 3 hours

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Q. Two pipes can fill a tank in 6 hours and 9 hours respectively. How long will it take to fill the tank if both pipes are opened together?

A. 2.5 hours
B. 3 hours
C. 3.5 hours
D. 4 hours

Solution

The combined rate is 1/6 + 1/9 = 3/18 + 2/18 = 5/18. Therefore, it will take 18/5 hours or 3.6 hours.

Correct Answer: B — 3 hours

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Q. Two pipes can fill a tank in 8 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 4.8 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/8 + 1/12 = 5/24. Therefore, time taken = 24/5 = 4.8 hours.

Correct Answer: A — 4.8 hours

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Q. Two pipes can fill a tank in 9 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 4.5 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/9 + 1/12 = 7/36. Therefore, it will take 36/7 = 5.14 hours to fill the tank.

Correct Answer: C — 6 hours

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Q. Two trains are moving towards each other at speeds of 60 km/h and 90 km/h. If they are 300 km apart, how long will it take for them to meet?

A. 1 hour
B. 2 hours
C. 3 hours
D. 4 hours

Solution

Time = Distance / (Speed of A + Speed of B) = 300 km / (60 + 90) km/h = 300 / 150 = 2 hours.

Correct Answer: B — 2 hours

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Q. Two trains are running in opposite directions at speeds of 50 km/h and 70 km/h. What is their relative speed?

A. 120 km/h
B. 100 km/h
C. 80 km/h
D. 90 km/h

Solution

Relative speed = Speed of train 1 + Speed of train 2 = 50 km/h + 70 km/h = 120 km/h.

Correct Answer: A — 120 km/h

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Q. Two trains start from the same point and travel in opposite directions. If one train travels at 80 km/h and the other at 100 km/h, how far apart will they be after 2 hours?

A. 360 km
B. 320 km
C. 280 km
D. 240 km

Solution

Distance = (Speed1 + Speed2) * Time = (80 km/h + 100 km/h) * 2 h = 360 km.

Correct Answer: A — 360 km

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Q. Two trains start from the same point and travel in opposite directions. One train travels at 60 km/h and the other at 90 km/h. How far apart will they be after 1 hour?

A. 150 km
B. 120 km
C. 90 km
D. 60 km

Solution

Distance apart = Speed of train 1 + Speed of train 2 = 60 km/h + 90 km/h = 150 km.

Correct Answer: A — 150 km

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Q. Two trains start from the same point and travel in opposite directions. Train A travels at 50 km/h and Train B at 70 km/h. How far apart will they be after 2 hours?

A. 240 km
B. 130 km
C. 140 km
D. 160 km

Solution

Distance = (Speed of A + Speed of B) * Time = (50 + 70) * 2 = 240 km.

Correct Answer: A — 240 km

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Q. Two trains start from the same point and travel in opposite directions. Train A travels at 80 km/h and Train B at 100 km/h. How far apart will they be after 1 hour?

A. 180 km
B. 160 km
C. 200 km
D. 150 km

Solution

Distance apart = (Speed of A + Speed of B) * Time = (80 + 100) * 1 = 180 km.

Correct Answer: A — 180 km

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Q. What day of the week was July 4, 1776?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday

Solution

Using Zeller's Congruence, July 4, 1776 falls on a Thursday.

Correct Answer: C — Wednesday

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Q. What day of the week will it be on December 31, 2023 if January 1, 2023 is a Sunday?

A. Saturday
B. Sunday
C. Monday
D. Tuesday

Solution

2023 has 365 days, which is 52 weeks and 1 day. December 31, 2023 will be one day before January 1, 2024, which is a Sunday, making it Saturday.

Correct Answer: A — Saturday

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Q. What day of the week will it be on December 31, 2025 if January 1, 2025 is a Wednesday?

A. Friday
B. Saturday
C. Sunday
D. Monday

Solution

2025 is not a leap year, so it has 365 days. From January 1 to December 31 is 364 days, which is 52 weeks + 0 days. Therefore, December 31, 2025 will also be a Wednesday.

Correct Answer: B — Saturday

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Q. What is 0.75 as a fraction?

A. 1/2
B. 3/4
C. 2/3
D. 1/4

Solution

0.75 = 75/100 = 3/4 after simplification.

Correct Answer: B — 3/4

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Q. What is 0.9 as a fraction?

A. 9/10
B. 1/10
C. 1/5
D. 1/2

Solution

0.9 = 9/10.

Correct Answer: A — 9/10

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Q. What is 15% of 0.4?

A. 0.06
B. 0.04
C. 0.05
D. 0.07

Solution

15% of 0.4 = 0.15 * 0.4 = 0.06

Correct Answer: A — 0.06

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Q. What is 15% of 0.6?

A. 0.09
B. 0.1
C. 0.08
D. 0.07

Solution

15% of 0.6 = 0.15 * 0.6 = 0.09

Correct Answer: A — 0.09

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Q. What is 15% of 200?

A. 25
B. 30
C. 35
D. 40

Solution

15% of 200 is calculated as (15/100) * 200 = 30.

Correct Answer: B — 30

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Q. What is 25% of 0.8?

A. 0.1
B. 0.2
C. 0.25
D. 0.3

Solution

25% of 0.8 = 0.25 * 0.8 = 0.2

Correct Answer: B — 0.2

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Q. What is 25% of 200?

A. 25
B. 50
C. 75
D. 100

Solution

25% of 200 is calculated as (25/100) * 200 = 50.

Correct Answer: B — 50

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Arithmetic Aptitude

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