Question 65

A sum of ₹3,400 is divided among P and Q in such a way that $$\frac{3}{4}$$ of P's share is equal to $$\frac{2}{3}$$ of Q's share. What is the positive difference between the shares of P and Q?

Solution

A sum of ₹3,400 is divided among P and Q in such a way that $$\frac{3}{4}$$ of P's share is equal to $$\frac{2}{3}$$ of Q's share.

P+Q = 3400 Eq.(i)

$$P\times\ \frac{3}{4} = Q\times\ \frac{2}{3}$$

$$\frac{P}{Q}=\frac{2}{3}\times\ \frac{4}{3}$$

$$\frac{P}{Q}=\frac{8}{9}$$

Let's assume P = 8y and Q = 9y. Eq.(ii)

Put Eq.(ii) in Eq.(i).

8y+9y = 3400

17y = 3400

y = 200

The positive difference between the shares of P and Q = 9y-8y

= y

= 200

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