On selling mangoes at 36 for a rupee, a shopkeeper loses 10%. How many mangoes…

CONCEPT: When a fixed number of items are sold for a fixed total amount (here, a rupee), the number of items bundled together is inversely linked to the price charged per item. If selling N items for that fixed amount causes a loss of L%, then to earn a gain of G% instead — with the same cost price per item — the new count N′ sold for the same fixed amount follows N′ = N × (100 − L) / (100 + G), because only the quantity bundled into the fixed revenue changes, not the cost per item.

1. Let the Cost Price (CP) of 36 mangoes be C. A 10% loss means the Selling Price of Rs. 1 equals 90% of C: 1 = (90/100) × C, so C = 10/9.

2. So the CP of 36 mangoes is Rs. 10/9, which gives CP per mango = 10 / (9 × 36) = 5/162.

3. To gain 8%, the Selling Price of n mangoes must equal 108% of the CP of n mangoes: 1 = (108/100) × (n × 5/162).

4. Solving, n = (100 × 162) / (108 × 5) = 16200 / 540 = 30.

CROSS-CHECK: Using the quick-transformation formula directly: n = 36 × (100 − 10) / (100 + 8) = 36 × 90/108 = 30, confirming the same result.

RESULT: The shopkeeper should sell 30 mangoes for a rupee to gain 8%.