Question

# Two years hence, the respective ratio between A's age at that time and B's age at that time will be 6:5. A's age 13 years ago was half of B's present age. What is A's present age?

A
16 years
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B
40 years
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C
28 years
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D
22 years
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E
34 years
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Solution

## The correct option is C 22 yearsLet the A's present age be x years and B's present age be y years. Then, according to the question, x+2y+2=65⇒5x+10=6y+12⇒5x−6y=12−10⇒5x−6y=2⇒5x−2=6y⇒5x−26=y⇒y=5x−26 (i)x−13=12y⇒x=12y+13⇒2x=y+26⇒2x=5x−26+26 [∵y=5x−26]⇒12x=5x−2+156⇒12x−5x=154⇒7x=154⇒x=22 Thus, present age of A = 22 years

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