Cost price of an article P is Rs. 500 less than that of Q. P and Q are marked 50% and 25% above their cost price respectively. P and Q are sold after allowing discounts of Rs. 300 and Rs. 200 respectively. Profit earned by P is Rs. 150 more than earned by Q. Find the marked price of P.

Solution

Let the cost price of Q be Rs. ‘a’ Cost price of P = Rs. (a − 500) Marked price of P
= 1.5 × (a − 500)
= Rs. (1.5a − 750) Marked price of Q
= 1.25 × a
= Rs. 1.25a Selling price of P
= 1.5a − 750 − 300
= Rs. (1.5a − 1050) Selling price of Q
= 1.25a − 200 Profit earned by P
= 1.5a − 1050 − a + 500
= Rs. (0.5a − 550) Profit earned by Q
= 1.25a − 200 − a
= Rs. (0.25a − 200) ATQ, 0.5a − 550 = 0.25a − 200 + 150 Or, 0.5a − 550 = 0.25a − 50 Or, 0.25a = 500 Or, a = 2000 Marked price of P
= 1.5 × 2000 − 750
= 3000 − 750
= Rs. 2,250