Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. The ratio of the lengths of two sides of a triangle is 3:4. If the perimeter is 70 cm, what is the length of the shorter side?

A. 30
B. 20
C. 25
D. 15

Solution

Let the sides be 3x and 4x. Then, 3x + 4x = 70, 7x = 70, x = 10. Shorter side = 3x = 3*10 = 30.

Correct Answer: B — 20

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Q. The ratio of the number of students in two classes is 4:5. If there are 36 students in the first class, how many students are in the second class?

A. 45
B. 40
C. 50
D. 36

Solution

Let the number of students in the first class be 4x and in the second class be 5x. Given 4x = 36, x = 9. Therefore, students in the second class = 5x = 5*9 = 45.

Correct Answer: A — 45

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Q. The ratio of the number of students in two classes is 5:6. If there are 60 students in the first class, how many students are in the second class?

A. 72
B. 66
C. 60
D. 54

Solution

Let students in the first class be 5x and in the second class be 6x. Given 5x = 60, x = 12. Therefore, students in the second class = 6x = 6*12 = 72.

Correct Answer: A — 72

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Q. The ratio of the speeds of two cars is 5:7. If the faster car travels 140 km in 2 hours, how far does the slower car travel in the same time?

A. 100
B. 120
C. 140
D. 160

Solution

Speed of faster car = 140 km / 2 hours = 70 km/h. Speed of slower car = (5/7) * 70 = 50 km/h. Distance traveled by slower car in 2 hours = 50 * 2 = 100 km.

Correct Answer: B — 120

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Q. The sum of the ages of A and B is 50 years. If A is 10 years older than B, how old is A?

A. 20
B. 25
C. 30
D. 35

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 50. Solving gives x = 20, hence A = 30.

Correct Answer: C — 30

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Q. The sum of the ages of A and B is 50 years. If A is 10 years older than B, what is B's age?

A. 20
B. 25
C. 30
D. 15

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 50. Solving gives x = 20.

Correct Answer: B — 25

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Q. The sum of the ages of a father and his son is 50 years. If the father is 30 years older than the son, how old is the son?

A. 10
B. 15
C. 20
D. 25

Solution

Let the son's age be x. Then the father's age is x + 30. So, x + (x + 30) = 50. Solving gives x = 10.

Correct Answer: C — 20

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Q. The sum of the ages of a father and his son is 50 years. If the father is 40 years old, how old is the son?

A. 10
B. 15
C. 20
D. 30

Solution

If the father is 40 years old, then the son is 50 - 40 = 10 years old.

Correct Answer: C — 20

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Q. The sum of the ages of a mother and her daughter is 50 years. If the mother is 4 times as old as her daughter, how old is the daughter?

A. 10
B. 8
C. 12
D. 6

Solution

Let the daughter's age be x. Then the mother's age is 4x. The equation is x + 4x = 50, which simplifies to 5x = 50, so x = 10.

Correct Answer: A — 10

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Q. The sum of the ages of a mother and her daughter is 60 years. If the daughter is 15 years old, how old is the mother?

A. 35
B. 40
C. 45
D. 50

Solution

If the daughter is 15 years old, then the mother is 60 - 15 = 45 years old.

Correct Answer: B — 40

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Q. The sum of the ages of a mother and her daughter is 60 years. If the daughter is 20 years old, how old is the mother?

A. 30
B. 40
C. 50
D. 20

Solution

If the daughter is 20 years old, then the mother is 60 - 20 = 40 years old.

Correct Answer: B — 40

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Q. The sum of the ages of a mother and her daughter is 60 years. If the mother is 36 years old, how old is the daughter?

A. 20
B. 24
C. 26
D. 30

Solution

If the mother is 36 years old, then the daughter's age is 60 - 36 = 24 years.

Correct Answer: B — 24

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Q. The sum of the ages of a mother and her daughter is 60 years. If the mother is 4 times as old as her daughter, how old is the daughter?

A. 8
B. 10
C. 12
D. 15

Solution

Let the daughter's age be x. Then the mother's age is 4x. So, x + 4x = 60. Solving gives x = 12.

Correct Answer: B — 10

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Q. Three pipes can fill a tank in 6, 8, and 12 hours respectively. If all three 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 1/6 + 1/8 + 1/12 = 1/3. Therefore, it will take 3 hours to fill the tank.

Correct Answer: B — 3 hours

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Q. Three years ago, a man was 5 times as old as his son. If the man is currently 38 years old, how old is his son now?

A. 6
B. 7
C. 8
D. 9

Solution

Let the son's age be x. Three years ago, the man was 35 and the son was x - 3. So, 35 = 5(x - 3). Solving gives x = 8.

Correct Answer: C — 8

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Q. Three years ago, A was 2 times as old as B. If B is currently 12 years old, how old is A now?

A. 18
B. 20
C. 24
D. 30

Solution

Three years ago, B was 12 - 3 = 9 years old. A was 2 * 9 = 18 years old. Now, A is 18 + 3 = 21 years old.

Correct Answer: B — 20

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Q. Three years ago, A was 5 times as old as B. If B is now 10 years old, how old is A now?

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

Solution

Three years ago, B was 7 years old. Therefore, A was 5 * 7 = 35 years old. Now, A is 35 + 3 = 38 years old.

Correct Answer: B — 30

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Q. Three years ago, A was 5 times as old as B. If B is now 7 years old, how old is A now?

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

Solution

Three years ago, B was 4 years old. Therefore, A was 5 * 4 = 20 years old. Now, A is 20 + 3 = 23 years old.

Correct Answer: B — 30

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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 15 hours and 25 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 1/15 + 1/25 = 5/75 + 3/75 = 8/75. Therefore, it will take 75/8 hours or 9.375 hours.

Correct Answer: B — 12 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. How long will it take to fill the tank if both pipes are opened together?

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

Solution

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

Correct Answer: C — 15 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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Arithmetic Aptitude

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