# Mrs Lata was 3 times as old as her son 8 years ago. Their total age is 64 years now. How old (in years) is Mrs Lata now?

This question was previously asked in
AWES 2019_Set E Official paper_Part A (PRT/TGT/PGT)
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1. 48
2. 12
3. 36
4. 44

Option 4 : 44

## Detailed Solution

Given:

Age of Mrs. Lata was 3 times as old as her son 8 years ago

Total age = 64 years

Calculation:

Let present age of Mrs. Lata = P years

The present age of son = Q years

∴ Their total age = 64 years

P + Q = 64       .... (i)

According to the question,

8 years ago, the present age of Mrs. Lata - 8 years = 3 × (present age of her son - 8 years)

⇒ P – 8 = 3 (Q – 8)

⇒ P – 8 = 3Q – 24

⇒ P – 3Q = – 16       ....(ii)

From equations (i) and (ii), we get

4Q = 80

⇒ Q = 20

Putting the value of Q in equation (i)

∴ Age of Mrs. Lata = 64 – 20 = 44 years
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