swerve wrote:Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage.

A. 16.8%
B. 17.4%
C. 17.9%
D. 18.5%
E. 19.1%

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Let's say that "a" represents apples and "o" represents oranges. Hence we now that $$a>o.$$ Now, let's say: $$P_a\ \ \ price\ per\ apple$$ $$P_o\ \ \ price\ per\ orange$$ "She sells apples at ₹23 apiece and makes 15% profit" this implies that $$23\cdot a=115\%\cdot a\cdot P_a\ \Rightarrow\ \ 1.15\cdot P_a=23\ \Rightarrow\ \ P_a=20.$$ "She sells oranges at ₹10 apiece and makes 25% profit" implies that $$10\cdot o=125\%\cdot o\cdot P_o\ \Rightarrow\ \ 1.25\cdot P_o=10\ \Rightarrow\ \ P_o=8.$$ Now, "she gets ₹653 after selling all the apples and oranges" implies that $$23\cdot a+10\cdot o=653\ \Rightarrow\ 10\cdot o=653-23\cdot a$$ hence, the units digit of 653-23a must be 0, therefore the units digit of "a" must be 1. Therefore, the options are 1, 11, 21, 31, . . . .

Now, since a>o, a=1 is not possible. If a=11 then "o" has to be equal to 30, which is not possible.

If a=21 then o=17 which is possible.

Now, the cost price is: $$20\cdot21+8\cdot17=420+136=556.$$ Since the cost price is 556 and she gets 653, then the percentage profit is: $$\frac{653-556}{556}\cdot100\%=\frac{97}{556}\cdot100\%=0.174\cdot100\%=17.4\%.$$ Therefore, the correct answer is B.

I hope it helps.