The ratio of present ages of P and Q is 3:8 and after 6 years their ages ratio is 4:9 then the age of P at present is …………….. years. 

A) 16 

B) 19

C) 18 

D) 20


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Correct option is (C) 18

Let present ages of P and Q are respectively 3x and 8x.

After 6 years, age of P = 3x+6,

age of Q = 8x+6.

According to given condition,

\(\frac{3x+6}{8x+6}=\frac49\)

\(\Rightarrow\) 9 (3x+6) = 4 (8x+6)

\(\Rightarrow\) 27x + 54 = 32x + 24

\(\Rightarrow\) 32x - 27x = 54 - 24

\(\Rightarrow\) 5x = 30

\(\Rightarrow\) \(x=\frac{30}5=6\)

\(\therefore\) Present age of P = 3x = 18 years.

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