The total cost price of a watch and a fan is Rs. 1,170. Rama sells the watch at a profit of 20% and the fan at a profit of 25%. If he earns a total profit of Rs. 265, then the cost price of watch is:

Explanation

Given: The total cost price of a watch and a fan is Rs. 1,170. Rama sells the watch at a profit of 20% and the fan at a profit of 25% Rama earns a total profit of Rs. 265. Concept used: P = S.P - C.P S.P = C.P × (100 ± P/L)/100 P% = (P/C.P) × 100 Where, C.P = Cost Price, S.P = Selling price, P = Profit Calculation: Let the C.P of a watch be Rs. x and The C.P of a fan is 1170 - x. According to the Question, Rama sells the watch at a profit of 20% S.P = C.P × (100 ± P/L)/100 ⇒ x × (100 + 20)/100 ⇒ x × 120/100 = 6/5 x Profit on Watch = 6/5 x - x ⇒ x/5 Rama sells the fan at a profit of 25% S.P = C.P × (100 ± P/L)/100 ⇒ (1170 - x) × (100 + 25)/100 ⇒ (1170 - x) × 125/100 = (1170 - x) × 5/4 Profit on the fan = [(1170 - x) × 5/4] - (1170 - x) ⇒ (1170 - x)/4 Now, If he earns a total profit of Rs. 265 ⇒ x/5 + (1170 - x)/4 = 265 ⇒ [4 x + (1170 × 5) - 5 x] / 20 = 265 ⇒ x = 550 ∴ The Required answer is Rs. 550. Shortcut Trick Let the cost price of the watch be Q. so, the price of the fan = (1170 - Q) According to the question, Q × 20% + (1170 - Q) × 25% = 265 ⇒ 0.2Q + 292.5 - 0.25Q = 265 ⇒ 0.05Q = 27.5 ⇒ Q = 27.5/0.05 ⇒ Q = 550 ∴ The cost price of the watch is Rs. 550.