Question 141

If the ages of P and R added to twice the age of Q ,the total becomes 59 .If the age of Q and R are added to thrice age of P,the total becomes 68 and if the age of the P is added to thrice age of Q and thrice the age age of R the total becomes 108 .What is the age of P?

Solution

Let ages of P,Q and R be $$p,q,r$$ respectively

According to ques, => $$(p+r)+2q=59$$ ------------(i)

and $$(q+r)+3p=68$$ -------------(ii)

and $$p+3q+3r=108$$ ------------(iii)

Multiplying equation (ii) by 3, => $$3q+3r+9p = 204$$ ----------(iv)

Subtracting equation (iii) from (iv), we get :

=> $$(9p-p)=(204-108)$$

=> $$8p=96$$

=> $$p=\frac{96}{8}=12$$ years

=> Ans - (D)

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