If a man sells 15 oranges for Rs.10 each, he gets a loss of x % and if he sell…
2025
If a man sells 15 oranges for Rs.10 each, he gets a loss of x % and if he sell at Rs. 12 each, he makes a profit of x %. Find x?
- A.
9.09
- B.
8.79
- C.
8.99
- D.
8.56
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Correct answer: A
Key idea: eliminate the cost price by forming two equations using the given selling prices and equal percentage loss/profit.
Let C be the cost price of 15 oranges.
When sold at Rs.10 each, SP = 15 × 10 = 150. A loss of x% gives: C × (100 - x)/100 = 150.
When sold at Rs.12 each, SP = 15 × 12 = 180. A profit of x% gives: C × (100 + x)/100 = 180.
Divide the two equations to eliminate C: 150/(100 - x) = 180/(100 + x).
Simplify: 5(100 + x) = 6(100 - x) → 500 + 5x = 600 - 6x → 11x = 100.
Thus x = 100/11 ≈ 9.09%.
Answer: 9.09%