A watch is sold at 16% profit. If this watch is bought at 10% less price and sold at a lower price of Rs. 14, then there is a profit of 25%. Find the cost price of a watch?

Given: A watch is sold at 16% profit.If this watch is bought at 10% less price and sold at a lower price of Rs. 14, then there is a profit of 25%.Concept: CP = [100/(100 + gain%)] × SP SP = [(100 + gain%)/100] × CPCalculation: Let the cost price of the watch is X rupeeSP = [(100 + 16)/100] × x⇒ 116x/100 According to questionWatch is bought at 10% less price New CP = x - x × 10%⇒ x - x/10⇒ 9x/10Now, watch is sold at 14 rupee lower price New SP = 116x/100 - 14 then, profit is 25%Also, New SP = [(100 + 25)/100] × 9x/10⇒ 5/4 × 9x/10⇒ 9x/8 Now, EQUATE both new selling price⇒ 116x/100 -14 = 9x/8⇒ 116x/100 - 9x/8 = 14⇒ (232x - 225x)/200 = 14⇒ 7x = 14 × 200⇒ x = 400∴ The cost price of watch is 400 rupee. Alternate Method: Let the cost price of the watch is 100 units. Then, SP = 100 + 100 × 16%⇒ 100 + 16⇒ 116 unitsAccording to the question,New CP = 100 - 100 × 10%⇒ 100 - 10⇒ 90 unitsNew Profit% = 25%New SP = 90 + 90 × 25%⇒ 90 + 22.5⇒ 112.5 unitsThe difference between both SP is 14 rupees given Difference in units = 116 - 112.5⇒ 3.5 unitsSo, 3.5 units = 14 rupee⇒ 1 unit = 14/3.5⇒ 4 rupeeCP = 100 units⇒ 100 × 4⇒ 400 rupee∴ The cost price of the watch is 400 rupees.