Arithmetic Aptitudes › Problems on Ages › Question #4433
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QWhat are the present ages of the elder person if the difference in ages between the two people is 16 years and the elder person was 3 times as old as the younger person 6 years ago?

ID: #4433 Problems on Ages 216 views
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  • A 48 ✔ ✖
  • B 25 ✔ ✖
  • C 30 ✔ ✖
  • D 36 ✔ ✖
Correct Answer: Option C

Explanation

If the difference in ages between the two people is 16 years,
 then the elder person is 16 years older than the younger person.
 Let X be the present age of the younger person. The elder person is X + 16 years old.

Six years ago, the elder person was X + 16 - 6 = X + 10 years old.

At that time, the elder person was 3 times as old as the younger person, 
so the younger person was (X + 10)/3 years old.

Six years ago, the younger person was X - 6 years old,
 so we can set up the following equation:

(X + 10)/3 = X - 6

Solving this equation gives us X = 14.

The present age of the younger person is 14 years,
 so the present age of the elder person is 14 + 16 = 30 years.

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