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.

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

Hint:

When two items have different profit percentages, always convert selling prices to cost prices first. Then use a linear equation for the total selling price to determine quantities and calculate overall profit percentage.

Answer 1

The Correct Option is B

Step 1: Find the cost price of one apple.
Selling price of one apple = Rs.\ 23, Profit = 15%. \[ \text{CP of 1 apple} = \frac{SP}{1+0.15} = \frac{23}{1.15} = 20 \ \text{Rs.} \] Step 2: Find the cost price of one orange.
Selling price of one orange = Rs.\ 10, Profit = 25%. \[ \text{CP of 1 orange} = \frac{SP}{1+0.25} = \frac{10}{1.25} = 8 \ \text{Rs.} \] Step 3: Let quantities of apples and oranges be \(x\) and \(y\).
Total selling price is given as Rs.\ 653: \[ 23x + 10y = 653 \] Step 4: Solve for integer solution with \(x>y\).
Modulo check: \[ 23x \equiv 653 \pmod{10} \;\Rightarrow\; 3x \equiv 3 \pmod{10} \;\Rightarrow\; x \equiv 1 \pmod{10}. \] So \(x=1,11,21,31,\dots\). Try \(x=21\): \[ 23(21) = 483 \quad \Rightarrow \quad 653 - 483 = 170 \quad \Rightarrow y=17. \] Thus, \(x=21, y=17\). Condition \(x>y\) satisfied. Step 5: Find total CP and profit.
Total SP = 653. \[ \text{Total CP} = 21(20) + 17(8) = 420 + 136 = 556. \] Profit = \(653 - 556 = 97\). \[ \text{Profit%} = \frac{97}{556}\times 100 \approx 17.44%. \] \[ \boxed{17.4%} \]