Problems On Ages - Study Mode

[#1] The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Correct Answer

(B) 16, 28, 36

Explanation

Solution: Let their present ages be 4 x , 7 x and 9 x years respectively. Then, (4 x - 8) + (7 x - 8) + (9 x - 8) = 56 ⇒ 20 x = 80 ⇒ x = 4 ∴ Their present ages are 4 x = 16 years, 7 x = 28 years and 9 x = 36 years respectively.

[#2] Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Correct Answer

(C) 6 years

Explanation

Solution: Mother's age when Ayesha's brother was born = 36 years. Father's age when Ayesha's brother was born = (38 + 4) years = 42 years. ∴ Required difference = (42 - 36) years = 6 years.

[#3] A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
Correct Answer

(C) 40 years

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{mother's}},{ ext{present}},{ ext{age}},{ ext{be}},x,{ ext{years}}{ ext{.}} cr
& { ext{Then,}},{ ext{the}},{ ext{person's}},{ ext{present}},{ ext{age}} cr
& = {frac{2}{5}x} ,,{ ext{years}} cr
& herefore {frac{2}{5}x + 8} = frac{1}{2}left( {x + 8}
ight) cr
& Rightarrow 2left( {2x + 40}
ight) = 5left( {x + 8}
ight) cr
& Rightarrow x = 40 cr} $$

[#4] Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
Correct Answer

(D) Data inadequate

Explanation

Solution: Given that: 1. The difference of age b/w R and Q = The difference of age b/w Q and T. 2. Sum of age of R and T is 50 i.e. (R + T) = 50. Question: R - Q = ?. Explanation: R - Q = Q - T (R + T) = 2Q Now given that, (R + T) = 50 So, 50 = 2Q and therefore Q = 25. Question is (R - Q) = ? Here we know the value(age) of Q (25), but we don't know the age of R. Therefore, (R-Q) cannot be determined.

[#5] The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Correct Answer

(B) 7 : 3

Explanation

Solution: Let the ages of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] ⇒ 3x + 20 = 2x + 40 ⇒ x = 20 ∴ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3