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### Question

A profit of 50%, as calculated on the cost price, is made by selling an item for Rs. 39. What is the profit in rupees?

**A**

Rs. 13.

**B**

Rs. 14.

**C**

Rs. 12.

**D**

Rs. 15.

**Soln.**

**Ans: a**

If cost is C, profit is P% and sale is S, then we know that C = $S/(1 + P/100)$. So the profit in rupees would be S - C = S - $S/(1 + P/100)$, which simplifies to ${S × P}/{100 + P}$, which is ${39 × 50}/{100 + 50}$ = Rs. 13.

__Shortcut Method__: If sale is 150, profit is Rs. 50. So if sale is 39, profit = Rs. $50/150$ × 39 = Rs. 13.