Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. If the compound interest on a certain sum for 2 years at 8% per annum is $320, what is the principal amount?

A. $4000
B. $5000
C. $6000
D. $8000

Solution

Let P be the principal. CI = P[(1 + r)^n - 1] = P[(1 + 0.08)^2 - 1] = P[0.1664]. Thus, 320 = P * 0.1664, P = $5000.

Correct Answer: B — $5000

Q. If the length of a rectangle is doubled and the width is halved, how does the area change?

A. Remains the same
B. Doubles
C. Halves
D. Quadruples

Solution

New area = (2 × length) × (width/2) = length × width = original area. Area doubles.

Correct Answer: B — Doubles

Q. If the present age of a father is 45 years and his son is 15 years old, in how many years will the father be twice as old as his son?

A. 10
B. 15
C. 20
D. 5

Solution

Let the number of years be x. In x years, the father's age will be 45 + x and the son's age will be 15 + x. The equation is 45 + x = 2(15 + x), which simplifies to 45 + x = 30 + 2x, so x = 15.

Correct Answer: A — 10

Q. If the present age of a grandfather is 80 years and the age of his grandson is 20 years, how many years ago was the grandfather 3 times as old as the grandson?

A. 10
B. 20
C. 30
D. 40

Solution

Let x years ago, grandfather's age was 80 - x and grandson's age was 20 - x. We need 80 - x = 3(20 - x). Solving gives x = 10.

Correct Answer: B — 20

Q. If the present age of a man is 3 times that of his son and the sum of their ages is 48 years, what is the age of the son?

A. 8
B. 12
C. 16
D. 20

Solution

Let the son's age be x. Then the man's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

Q. If the present age of a man is 4 times that of his son, and after 5 years, the man will be 3 times as old as his son. What is the present age of the son?

A. 5
B. 10
C. 15
D. 20

Solution

Let the son's age be x. Then the man's age is 4x. In 5 years, 4x + 5 = 3(x + 5). Solving gives x = 10.

Correct Answer: B — 10

Q. If the present age of a mother is 4 times that of her daughter and the daughter is 5 years old, what is the mother's age?

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

Solution

If the daughter is 5 years old, then the mother is 4 * 5 = 20 years old.

Correct Answer: C — 25

Q. If the present age of a mother is 4 times that of her son, and the son is 5 years old, what will be the mother's age in 5 years?

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

Solution

The mother is currently 4 * 5 = 20 years old. In 5 years, she will be 20 + 5 = 25 years old.

Correct Answer: B — 25

Q. If the present age of a woman is 5 years more than twice the age of her son, and the son is currently 10 years old, what is the age of the woman?

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

Solution

The son's age is 10. Therefore, the woman's age is 2 * 10 + 5 = 20 + 5 = 25.

Correct Answer: A — 25

Q. If the present age of C is 3 times that of D and the sum of their ages is 48, what is the present age of D?

A. 8
B. 12
C. 16
D. 20

Solution

Let D's age be x. Then C's age is 3x. So, x + 3x = 48, which gives 4x = 48, hence x = 12.

Correct Answer: C — 16

Q. If the present age of C is 3 times that of D, and D is 8 years old, what is C's age?

A. 20
B. 24
C. 30
D. 32

Solution

If D is 8 years old, then C is 3 * 8 = 24 years old.

Correct Answer: B — 24

Q. If the present age of C is 3 times that of D, and the sum of their ages is 48 years, what is D's age?

A. 8
B. 12
C. 16
D. 20

Solution

Let D's age be x. Then C's age is 3x. So, x + 3x = 48, which gives 4x = 48, hence x = 12.

Correct Answer: B — 12

Q. If the present age of C is 4 years more than D, and D is 12 years old, what is the present age of C?

A. 14
B. 16
C. 12
D. 10

Solution

If D is 12 years old, then C is 12 + 4 = 16 years old.

Correct Answer: A — 14

Q. If the present age of E is 5 years more than F and the sum of their ages is 55, what is E's age?

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

Solution

Let F's age be x. Then E's age is x + 5. So, x + (x + 5) = 55, which gives 2x + 5 = 55, hence 2x = 50, x = 25. Therefore, E's age is 25 + 5 = 30.

Correct Answer: C — 35

Q. If the present value of a bill is Rs. 7200 and the bankers' discount is Rs. 800, what is the face value of the bill?

A. Rs. 8000
B. Rs. 7200
C. Rs. 6000
D. Rs. 5000

Solution

Face Value = Present Value + BD = 7200 + 800 = Rs. 8000.

Correct Answer: A — Rs. 8000

Q. If the present value of a sum is $4500 and the bankers discount is $500, what is the principal?

A. $5000
B. $5500
C. $6000
D. $6500

Solution

Principal = Present Value + Bankers Discount = 4500 + 500 = $5000.

Correct Answer: A — $5000

Q. If the principal is $15000 and the bankers discount is $2250, what is the rate of interest?

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

Solution

Rate = (Bankers Discount × 100) / (Principal × Time) = (2250 × 100) / (15000 × 1) = 15%.

Correct Answer: A — 10%

Q. If the radius of a circle is 7 cm, what is its area? (Use π = 22/7)

A. 154 cm²
B. 44 cm²
C. 77 cm²
D. 88 cm²

Solution

Area = π × radius² = (22/7) × (7 cm)² = 154 cm².

Correct Answer: A — 154 cm²

Q. If the ratio of boys to girls in a class is 3:2 and there are 30 students, how many girls are there?

A. 10
B. 12
C. 18
D. 20

Solution

Let the number of boys be 3x and girls be 2x. Then, 3x + 2x = 30, which gives 5x = 30, so x = 6. Therefore, the number of girls is 2x = 12.

Correct Answer: B — 12

Q. If the ratio of boys to girls in a class is 3:4 and there are 28 girls, how many boys are there?

A. 21
B. 24
C. 25
D. 30

Solution

Let the number of boys be 3x and girls be 4x. Given 4x = 28, we find x = 7. Thus, boys = 3x = 3*7 = 21.

Correct Answer: A — 21

Q. If the sum of the ages of A and B is 60 years and A is 10 years older than B, how old is A?

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

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 60. Solving gives x = 25, hence A = 35.

Correct Answer: C — 35

Q. If the sum of the ages of A and B is 60 years and A is 10 years older than B, what are their ages?

A. 25, 35
B. 30, 30
C. 20, 40
D. 35, 25

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 60. Solving gives x = 25. Therefore, A is 35 and B is 25.

Correct Answer: A — 25, 35

Q. If the true discount on a bill of Rs. 3000 due in 5 months is Rs. 150, what is the Banker's Discount at 10% per annum?

A. Rs. 200
B. Rs. 150
C. Rs. 250
D. Rs. 300

Solution

Banker's Discount = True Discount * (1 + (Rate * Time)) = 150 * (1 + (10 * 5/12)) = Rs. 200.

Correct Answer: A — Rs. 200

Q. If today is April 15, what will be the date after 100 days?

A. July 24
B. July 25
C. July 26
D. July 27

Solution

April has 15 days left after April 15. 100 - 15 = 85 days left. May has 31 days, June has 30 days, and July has 24 days. 15 + 31 + 30 + 24 = 100. So, the date will be July 25.

Correct Answer: B — July 25

Q. If today is Friday, what day will it be 50 days from now?

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

Solution

50 days = 7 weeks + 1 day. Therefore, it will be Saturday, which is 1 day after Friday.

Correct Answer: C — Monday

Q. If today is July 4, 2023, what will be the date 200 days from now?

A. January 20, 2024
B. January 21, 2024
C. January 22, 2024
D. January 23, 2024

Solution

From July 4 to July 31 is 27 days. August has 31 days, September has 30 days, October has 31 days, November has 30 days, December has 31 days, and January has 31 days. 27 + 31 + 30 + 31 + 30 + 31 + 20 = 200 days. Thus, it will be January 20, 2024.

Correct Answer: A — January 20, 2024

Q. If today is March 15, 2023, what will be the date after 100 days?

A. June 23, 2023
B. June 24, 2023
C. June 25, 2023
D. June 26, 2023

Solution

March has 31 days, so from March 15 to March 31 is 16 days. April has 30 days, May has 31 days, and June has 30 days. 16 + 30 + 31 + 23 = 100 days. Therefore, the date will be June 24, 2023.

Correct Answer: B — June 24, 2023

Q. If today is October 10, 2023, what will be the date 50 days from now?

A. November 29, 2023
B. November 30, 2023
C. December 1, 2023
D. December 2, 2023

Solution

From October 10 to October 31 is 21 days. November has 30 days. 50 - 21 = 29 days left in November. Thus, it will be November 30, 2023.

Correct Answer: B — November 30, 2023

Q. If today is the 15th of a month, what is the maximum number of days left in that month?

A. 14
B. 15
C. 16
D. 17

Solution

The maximum number of days in a month is 31. If today is the 15th, there are 31 - 15 = 16 days left.

Correct Answer: A — 14

Q. If today is the 1st of a month and it has 31 days, what will be the day of the week on the 31st of that month?

A. Same as today
B. One day later
C. Two days later
D. Three days later

Solution

31 days = 4 weeks + 3 days. Therefore, the day on the 31st will be three days later than the 1st.

Correct Answer: B — One day later

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