A man purchased some oranges at 4 oranges for ₹7 and sold them at 7 oranges…
2023
A man purchased some oranges at 4 oranges for ₹7 and sold them at 7 oranges for ₹13. Thus, he gained ₹30 in all. The number of oranges he bought is
Answer: B. 280 — ConceptWhen goods are bought and sold in groups, first convert each group rate into a per-item cost price and selling price. Profit per item equals selling…
- A.
252
- B.
280
- C.
308
- D.
336
Show answer & explanation
Correct answer: B
Concept
When goods are bought and sold in groups, first convert each group rate into a per-item cost price and selling price. Profit per item equals selling price per item minus cost price per item, and total profit equals profit per item multiplied by the number of items.
Application
Cost price per orange = ₹7 ÷ 4 = ₹7/4.
Selling price per orange = ₹13 ÷ 7 = ₹13/7.
Profit per orange = ₹13/7 − ₹7/4 = ₹(52 − 49)/28 = ₹3/28.
Let n be the number of oranges. Then n × ₹3/28 = ₹30, so n = 30 × 28 ÷ 3 = 280.
Cross-check
For 280 oranges, the purchase cost is 280 × ₹7/4 = ₹490 and the sale proceeds are 280 × ₹13/7 = ₹520. Their difference is ₹30, matching the stated total profit.
Therefore, the man bought 280 oranges.