By selling 35 eggs for Rs 30, a man loses 25%. How many eggs should he sell…
2024
By selling 35 eggs for Rs 30, a man loses 25%. How many eggs should he sell for Rs 144 to gain 20%?
Answer: C. 105 — ConceptWhen an item is sold at a loss of L%, its selling price is (100 − L)% of its cost price. When it is sold at a profit of P%, its selling price is (100 +…
- A.
85
- B.
95
- C.
105
- D.
115
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
When an item is sold at a loss of L%, its selling price is (100 − L)% of its cost price. When it is sold at a profit of P%, its selling price is (100 + P)% of its cost price. Recover the unit cost first, apply the desired profit rate, and then divide the target selling amount by the new selling price per unit.
Application
For 35 eggs, Rs 30 is 75% of their cost price. Therefore, the cost price of 35 eggs is Rs 30 × 100/75 = Rs 40.
The cost price per egg is Rs 40/35 = Rs 8/7.
At a 20% profit, the required selling price per egg is Rs (8/7) × 120/100 = Rs 48/35.
The number of eggs sold for Rs 144 is 144 ÷ (48/35) = 144 × 35/48 = 105.
Cross-check
The cost of 105 eggs is Rs 105 × 8/7 = Rs 120. Selling them for Rs 144 gives a profit of Rs 24, and (24/120) × 100 = 20%.
Therefore, he should sell 105 eggs for Rs 144.