The income of P and Q are in the ratio 3:2 and expenses are in the ratio 5:3. If both save Rs. 200, what is the income of P? 

Correct option is (D) Rs. 1200

Let 3x and 2x are income of P and Q respectively.

And 5y and 3y are expenses of P and Q respectively.

\(\therefore\) Saving of P = 3x - 5y

Saving of Q = 2x - 3y

Given that both P and Q save Rs 200.

\(\therefore\) 3x - 5y = 200        ___________(1)

And 2x - 3y = 200    ___________(2)

Multiply equation (1) by 2 & equation (2) by 3, we get

6x - 10y = 400         ___________(3)

6x - 9y = 600           ___________(4)

Subtract equation (3) from (4), we obtain

(6x - 9y) - (6x - 10y) = 600 - 400

\(\Rightarrow\) -9y + 10y = 200

\(\Rightarrow\) y = 200

Then from (2), we have

\(x=\frac{200+3y}2=\frac{200+600}2\)

\(\Rightarrow\) \(x=\frac{800}2=400\)

\(\therefore\) Income of P = 3x

\(=3\times400\) = Rs 1200

Correct option is D) Rs. 1200