The Ages of the Two Persons Differ by 20 Years. If 5 Year Ago, The Older GMAT Problem Solving

Question: The ages of the two persons differ by 20 years. If 5 year ago, the older one was 5 times as old as the younger one, then their present ages, in year are:

1. 25, 5
2. 30, 10
3. 35, 15
4. 50, 30
5. 50, 30

Answer: B
Solution and Explanation:
Approach Solution 1:

Given to us that the difference between the ages of two persons are 20 years. Also given that 5 years ago the older one was 5 times as old as the younger one, then their present ages are asked.
"The ages of the two persons differ by 20 years": Then we should set the variables x and x+20.
5 years ago, the age of the two people would be x−5 and x+15
If 5 years ago, the older one was 5 times as old as the younger one: Clearly, x + 15 is the older one. Then x+15 = 5(x−5)
4x = 40 and x = 10
The age of the younger one is 10 years, and hence the age of the elder will be 30 years.
B is the correct answer.

Correct Answer: B

Approach Solution 2:

Let the present ages of the older and the younger persons be A and B years respectively.
The difference in their ages is 20 years. Therefore, A – B = 20
Five years ago, age of the older one = A – 5 years and age of the younger one = B – 5 years.
It is told that, five years ago, the older one was 5 times as old as the younger one. Therefore,
(A – 5) = 5 (B – 5)
From A – B = 20, we can say A = B + 20. Substituting this value of A in the equation above, we have, [(B + 20) – 5] = 5 (B -5).
Simplifying, B + 15 = 5B – 25.
Solving for B, we have 4B = 40 OR B = 10.
Therefore, A = B + 20 = 10 + 20 = 30.
Their present ages are 30 and 10.
The correct answer option is B.

Correct Answer: B

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