Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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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 45 km/h and 55 km/h. If they are 200 km apart, how long will it take for them to meet?

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

Solution

Relative speed = 45 + 55 = 100 km/h. Time = Distance / Speed = 200 km / 100 km/h = 2 hours.

Correct Answer: B — 2 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 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. One train travels at 60 km/h and the other at 90 km/h. How far apart will they be after 2 hours?

A. 300 km
B. 240 km
C. 180 km
D. 150 km

Solution

Distance = (Speed1 + Speed2) x Time = (60 km/h + 90 km/h) x 2 h = 300 km

Correct Answer: A — 300 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. 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, A and B, are moving in opposite directions at speeds of 50 km/h and 70 km/h respectively. If they are 200 km apart, how long will they take to meet?

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

Solution

Relative speed = 50 km/h + 70 km/h = 120 km/h. Time = Distance / Speed = 200 km / 120 km/h = 1.67 hours.

Correct Answer: B — 2 hours

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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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Q. What is log10(0.01)?

A. -2
B. -1
C. 0
D. 1

Solution

log10(0.01) = -2, since 10^-2 = 0.01.

Correct Answer: A — -2

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Q. What is log4(16)?

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

Solution

log4(16) = 2, since 4^2 = 16.

Correct Answer: B — 2

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Q. What is the angle between the hour and minute hand at 12:30?

A. 165 degrees
B. 180 degrees
C. 150 degrees
D. 135 degrees

Solution

At 12:30, the hour hand is at 165 degrees (12 hours * 30 degrees + 30 minutes * 0.5 degrees) and the minute hand is at 180 degrees (30 minutes * 6 degrees). The angle between them is |165 - 180| = 15 degrees.

Correct Answer: A — 165 degrees

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Q. What is the angle between the hour and minute hand at 12:45?

A. 135 degrees
B. 150 degrees
C. 165 degrees
D. 180 degrees

Solution

At 12:45, the hour hand is at 337.5 degrees (12 hours * 30 degrees + 45 minutes * 0.5 degrees) and the minute hand is at 270 degrees (45 minutes * 6 degrees). The angle between them is |337.5 - 270| = 67.5 degrees.

Correct Answer: B — 150 degrees

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Q. What is the angle between the hour and minute hand at 5:25?

A. 135 degrees
B. 150 degrees
C. 165 degrees
D. 180 degrees

Solution

At 5:25, the hour hand is at 162.5 degrees (5 hours * 30 degrees + 25 minutes * 0.5 degrees) and the minute hand is at 150 degrees (25 minutes * 6 degrees). The angle between them is |162.5 - 150| = 12.5 degrees.

Correct Answer: C — 165 degrees

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Q. What is the angle between the hour and minute hands at 12:30?

A. 165 degrees
B. 180 degrees
C. 150 degrees
D. 120 degrees

Solution

At 12:30, the hour hand is at 165 degrees (12*30 + 30*0.5) and the minute hand is at 180 degrees. The angle between them is |165 - 180| = 15 degrees.

Correct Answer: A — 165 degrees

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Arithmetic Aptitude

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