A man sells a watch for ₹1,140 and loses 5%. At what price should he sell it to gain 5%?
₹1,260. ₹1,140 is 95% of cost, so cost = 1,140 / 0.95 = ₹1,200. To gain 5%, sell at 1.05 x 1,200 = ₹1,260. Directly: 1,140 x 105/95 = 1,260.
Explain it simply
Both selling prices are percentages of the same cost price. At a 5% loss he gets 95 parts; at a 5% gain he gets 105 parts. If 95 parts are ₹1,140, one part is ₹12, so 105 parts are ₹1,260. You never need the cost price separately, though it is easy to find.
Example
Question: SP = ₹1,140 at a 5% loss. Find the SP for a 5% gain.
- 95% of CP = 1,140, so CP = 1,140 x 100 / 95 = ₹1,200.
- SP for 5% gain = 1,200 x 105 / 100 = ₹1,260.
One-step ratio: new SP = 1,140 x 105 / 95 = 12 x 105 = 1,260.
console.log((1140 * 105) / 95); // Output: 1260The same ratio method handles "sold at 8% gain for ₹540, what price gives 12% gain?": 540 x 112 / 108 = ₹560.
What to say in the interview
"Selling at a 5% loss means the price is 95% of cost, so cost is 1,200. A 5% gain needs 105% of cost, which is 1,260. Or in one line, 1,140 times 105 over 95."
Common mistakes
- Adding 10% to ₹1,140 (giving ₹1,254); the percentages are of cost, not of the old selling price.
- Taking 5% of ₹1,140 as the loss in rupees.