Question: Rani bought more apples than oranges. She sells apples at Rs. 23 apiece and makes 15% profit. She sells oranges at Rs. 10 apiece and marks 25% profit. If she gets Rs. 653 after selling all the apples and oranges, find her profit percentage.
Explanation:
Let the number of apples sold be ‘a’ and the number of oranges sold be ‘o’.
In R.H.S., there is a 3 in the unit’s place
∴ 23a + 10b should end with 3.
Now, unit’s digit of 10b will be ‘0’ hence units digit of 13a should be 3.
For this the values possible values of ‘a’ are 1, 11, 21, …
When a = 11, b = 40 [not possible since a should be more than b.]
When, a = 21, b = 17 which is in line with the condition of a > b
When a ≥ 31, b is negative, hence we will not consider those values.
∴ a = 21 and b = 17.
Now, the profit per apple is 15% and profit per orange is 25%
Cost price of each apple = 23/1.15 = Rs. 20
∴ Total Cost price = 20a + 8b = Rs.556
∴ Profit percent = ((653 - 556)/ 556) × 100 = 17.4%
Hence, option (b).