Question

A fruit seller buys some apples at the rate of 5 for Rupees 6 and an equal number more at 4 for Rupees 5. He sells the whole lot at 9 for Rupees 11. What is his loss or gain percent?

• A. loss $\dfrac{100}{441}$ \%
• B. gain $\dfrac{100}{441}$ \%
• C. No profit No loss
• D. Loss $\dfrac{5}{22}$ \%

Hint:

When equal numbers of items are bought at different rates, take the LCM of quantities to simplify calculations. Always compute total C.P. and S.P. carefully before calculating percentage profit or loss.

Answer 1

The Correct Option is A

Step 1: Assume number of apples.
Let the fruit seller buy 20 apples in the first case and 20 in the second case (equal numbers for convenience).
Step 2: Find cost price (C.P.) of first lot.
Rate = 5 apples for Rupees 6.
So, cost of 20 apples = \(\dfrac{20}{5} \times 6 = 4 \times 6 = Rupees\; 24\).
Step 3: Find cost price of second lot.
Rate = 4 apples for Rupees 5.
So, cost of 20 apples = \(\dfrac{20}{4} \times 5 = 5 \times 5 = Rupees \; 25\).
Step 4: Total cost price.
Total apples = 20 + 20 = 40.
Total C.P. = 24 + 25 = Rupees 49.
Step 5: Selling price (S.P.) of all apples.
Rate = 9 apples for Rupees 11.
So, S.P. of 40 apples = \(\dfrac{40}{9} \times 11 = \dfrac{440}{9} \approx Rupees 48.89\).
Step 6: Calculate loss.
Loss = C.P. - S.P. = \(49 - \dfrac{440}{9} = \dfrac{441 - 440}{9} = \dfrac{1}{9}\).
Step 7: Loss percentage.
\[ \text{Loss \%} = \dfrac{\text{Loss}}{\text{C.P.}} \times 100 = \dfrac{\tfrac{1}{9}}{49} \times 100 = \dfrac{100}{441} \%. \] \[\boxed{\text{Loss } \dfrac{100}{441} \%}\]