Radha sold a watch for Rs 144 and got a percentage of profit equal to the cost…
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Radha sold a watch for Rs 144 and got a percentage of profit equal to the cost price of the watch. What is the cost price of the watch ?
- A.
Rs 80
- B.
Rs 78
- C.
Rs 72
- D.
Rs 90
Attempted by 33 students.
Show answer & explanation
Correct answer: A
Let the cost price be x rupees. The profit percent equals x%, so the profit amount is x * (x/100) = x²/100.
Selling price = cost price + profit, so x + x²/100 = 144.
Multiply both sides by 100: x² + 100x = 14400, which gives the quadratic x² + 100x - 14400 = 0.
Solve using the quadratic formula: discriminant = 100² + 4·14400 = 67600, √discriminant = 260. Roots = (-100 ± 260)/2 = 80 or -180.
Discard the negative root. Therefore the cost price is Rs 80.