A person sold a watch at a profit of 17%. If he sold it for Rs. 417.60 more,…
2020
A person sold a watch at a profit of 17%. If he sold it for Rs. 417.60 more, he gained x%. If the cost price of the watch is Rs. 4570, then the value of x (to the nearest integer) is:
- A.
18
- B.
24
- C.
32
- D.
26
Show answer & explanation
Correct answer: D
For a fixed cost price (CP), the profit percentage p is defined by SP = CP × (1 + p/100), so the profit amount itself is (p/100) × CP. When the selling price is raised further by a fixed rupee amount while the CP stays the same, that extra amount, expressed as a percentage of the SAME CP, adds directly onto the earlier profit percentage — both profit figures share one base.
Applying this to the given values:
Cost price (CP) = Rs. 4570. At a 17% profit, the first selling price is CP + 17% of CP = 4570 + 776.90 = Rs. 5346.90.
Selling it for Rs. 417.60 more gives a new selling price of 5346.90 + 417.60 = Rs. 5764.50.
The new total profit amount is 5764.50 − 4570 = Rs. 1194.50.
The new gain percentage is (1194.50 ÷ 4570) × 100 ≈ 26.14%, which rounds to 26 (nearest integer).
Cross-check by the shortcut: since both profit figures are percentages of the same CP, the extra Rs. 417.60 alone contributes (417.60 ÷ 4570) × 100 ≈ 9.14 percentage points. Adding this to the original 17% gives 17 + 9.14 ≈ 26.14%, the same result by an independent route.
So x = 26.