Q 1- The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. The present age of the father is:

A - 36 years

B - 25 years

C - 29 years

D - 40 years

Answer - A Explanation "Let father's present age = p years. Then, son's present age = (45 - p) years. ∴ (p - 5)(45 - p - 5) = 4(p - 5) or, p2 - 41p + 180 = 0 or, (p - 36)(p - 5) = 0 or, p = 36 years. "

Q 2-Sagar was twice as old as Anand 10 years back. How old is Anand today if Sagar will be 40 years old 10 years hence ?

A - 10 years

B - 20 years

C - 15 years

D - 30 years

Answer - B Explanation "Let Anand's age 10 years back be p years. Then, Sagar's age 10 years back = 2p years. ∴ 2p + 20 = 40 or, p = 10. Anand's present age = (p + 10) = (10 + 10) = 20 years. "

Q 3- Mamta got married 6 years ago. Today her age is 5/4 times her age at the time of marriage. His son's age is 1/10 times her age. The age of her son is:

A - 2 years

B - 4 years

C - 5 years

D - 3 years

Answer - D Explanation "Let son's age be p. Then, Mamta's age = 10p years. Mamta's age at the time of marriage = (10p - 6) years. ∴ 10p = 5/4(10p - 6) or,40p = 50p - 30 or, p = 3 years. "

Q 4- In 10 years, X will be twice as old as Y was 10 years ago. If X is now 9 years older than Y, the present age of Y is:

A - 49 years

B - 29 years

C - 19 years

D - 39 years

Answer - Explanation "Let the present ages of Y and X be p and (p + 9) years. ∴ (p + 9 + 10) = 2(p - 10) or, p = 39 years."

Q 5- Manoj is twice as old as Deepak and half as old as Suredra. If the sum of Suredra's and Deepak's ages is 85 years,what is Manoj's age in years ?

A - 24 years

B - 34 years

C - 36 years

D - 28 years

Answer - B Explanation "Let Deepak's age be p years. Then, Manoj's age be 2p years and Suredra's age be 4p years. ∴ Manoj's age = [2p / (p + 4p)] × 85 = 34 years. "

Q 6-The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the sum of the ages of his sons. The father's present age is:

A - 45 years

B - 50 years

C - 40 years

D - 55 years

Answer - A Explanation "Let the sum of present ages of the two sons be p years. Then, father's present age = 3p years. ∴ (3p + 5) = 2(p + 10) or, p = 15. Hence, father's present age = 45 years"

Q 7- A man's age is 150% of what it was 10 years ago, but 75% of what it will be after 10 years. What is his present age ?

A - 30 years

B - 25 years

C - 35 years

D - 40 years

Answer - A Explanation "Let the present age be p years. Then, 150% of (p - 10) = p and 75% of (p + 10) = p. ∴ 150% of (p - 10) = 75% of (p + 10) or, 6/4(p -10) = 3/4(p + 10) or, 6p - 60 = 3p + 30 or, p = 30 years."

Q 8- Rahul is 40 years old and Anand is 60 years old. How many years ago was the ratio of their ages 3:5.

A - 20 years

B - 37 years

C - 16 years

D - 10 years

Answer - D Explanation "Suppose, the ratio was 3:5, p years ago. Then, (40 - p)/(60 - p) = 3/5 or, 5(40 - p) = 3(60 - p) or, p = 10 years."

Q 9-. 6 years ago Sameer was twice as old as Deepak. If the ratio of their present ages is 9:5 respectively, what is the difference between their present ages in years ?

A - 30 years

B - 24 years

C - 50 years

D - 36 years

Answer - B Explanation "Let the present ages of Sameer and Deepak be 9p and 5p years respectively. Then, (9p - 6) = 2(5p - 6) or, p = 6. ∴ Difference = 9p - 5p = 4p = 4 × 6 = 24 years."

Q 10- Six years ago, the ratio of the ages of Jagunnath and Badri was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Badri's age at present ?

A - 12 years

B - 18 years

C - 16 years

D - 24 years

Answer - C Explanation "Let the ages of Jagunnath and Badri 6 years ago be 6p and 5p years respectively. Then, [(6p + 6) + 4] / [(5p + 6) + 4] = 11 / 10 or, 10(6p + 10) = 11(5p + 10) or, p = 2. ∴ Badri's present age = (5p + 6) = (5 × 2 + 6) = 16 years. "

Q 11-Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is:

A - 72 years

B - 105 years

C - 54 years

D - 108 years

Answer - D Explanation "Let the present ages of the father and son be 2p and p years respectively. Then, (2p - 18) = 3(p - 18) or, p = 36. ∴ Sum = (2p + p) = 3p = 3 × 36 = 108 years."

Q 12-At present the age of the father is 6 times the age of his son, 4 years hence the father's age would be 5 times that of his son. What is the sum of the present ages of father and his son ?

A - 114 years

B - 111 years

C - 112 years

D - 116 years

Answer - C Explanation "Let the present age of son be p years. Then, the present age of father = 6p years. After 4 years, son's age = (p+4) years and father's age = (6p+4) years. ∴ (6p + 4) = 5(p + 4) or, p = 16. ∴ Sum = (6p + p) = 7p = 7 × 16 = 112 years"

Q 13-The sum of the ages of a son and father is 56 years. After four years, the age of the father will be three times that of the son. Their ages respectively are:

A - 16 years, 48 years

B - 16 years, 42 years

C - 12 years, 44 years

D - 18 years, 36 years

Answer - C Explanation "Let the present age of son be p years. Then, the present age of father = (56 - p) years. After 4 years, son's age = (p+4) years and father's age = (56-p+4) years. ∴ (60 - p) = 3(p + 4) or, p = 12. ∴ Son's present age = 12 years and father's present age = 44 years"

Q 14-The age of Mr Arun is four times the age of his son. After ten years the age of Mr Arun will be only twice the age of his son. Find the present age of Mr Arun's son.

A - 5 years

B - 12 years

C - 8 years

D - 10 years

Answer - A Explanation "Let the present age of son be p years. Then, the present age of Mr Arun = 4p years. After 10 years, son's age = (p+10) years and Mr Arun's age = (4p+10) years. ∴ (4p + 10) = 2(p + 10) or, p = 5. ∴ Son's present age = p = 5 years."

Q 15-10 years ago Neelam's mother was 4 times older than her daughter. After 10 years, the mother will be twice older than the daughter. The present age of Neelam is:

A - 15 years

B - 20 years

C - 30 years

D - 10 years

Answer - B Explanation "Let the present age of Neelam's be p years and Neelam's mother age be q years. 10 years ago, Neelam's mother was 4 times older than her daughter. ∴ (q - 10) = 4(p - 10) or, q = (4p - 30) After 10 years, Neelam's mother will be twice older than her daughter. ∴ (q + 10) = 2(p + 10) or, q = (2p + 10) ∴ (4p - 30) = (2p + 10) or, p = 20 years."