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Ten yrs ago,the ages of the father and the son were in the ratio 6:1 and 10 yrs hence the ratio will become 2:1. The present age of the father is
  • a)
    35 yrs
  • b)
    25 yrs
  • c)
    30 yrs
  • d)
    40 yrs
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Ten yrs ago,the ages of the father and the son were in the ratio 6:1 a...
Let the present ages of the father and the son be F and S, respectively.
Ten years ago, the father's age was F - 10 and the son's age was S - 10.

According to the given information:
"The ages of the father and the son were in the ratio 6:1 ten years ago."
This can be written as:
(F - 10)/(S - 10) = 6/1
Cross-multiplying, we get:
1(F - 10) = 6(S - 10)
F - 10 = 6S - 60
F = 6S - 50 ----- (1)

"10 years hence the ratio will become 2:1."
This can be written as:
(F + 10)/(S + 10) = 2/1
Cross-multiplying, we get:
1(F + 10) = 2(S + 10)
F + 10 = 2S + 20
F = 2S + 10 ----- (2)

To find the present age of the father, we need to solve equations (1) and (2) simultaneously.

Substituting the value of F from equation (2) into equation (1), we get:
2S + 10 = 6S - 50
4S = 60
S = 15

Substituting the value of S = 15 into equation (2), we get:
F = 2(15) + 10
F = 40

Therefore, the present age of the father is 40 years, which corresponds to option (D).
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Ten yrs ago,the ages of the father and the son were in the ratio 6:1 and 10 yrs hence the ratio will become 2:1. The present age of the father isa)35 yrsb)25 yrsc)30 yrsd)40 yrsCorrect answer is option 'D'. Can you explain this answer?
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