Answer: C
Let the watch be purchased for \(x\) rupees. According to the question, selling the watch for 336 rupees gave him a profit of \(x\%\). ∴ A profit of \(x\) rupees on a cost price of 100 rupees means: On \(x\) rupees, the profit = \(\cfrac{x}{100} \times x = \cfrac{x^2}{100}\) rupees ∴ According to the question: \[ x + \cfrac{x^2}{100} = 336 \] \[ \cfrac{100x + x^2}{100} = 336 \] \[ 100x + x^2 = 33600 \] \[ x^2 + 100x - 33600 = 0 \] \[ x^2 + 240x - 140x - 33600 = 0 \] \[ x(x + 240) - 140(x + 240) = 0 \] \[ (x + 240)(x - 140) = 0 \] ∴ Either \((x + 240) = 0\) or \((x - 140) = 0\) When \((x + 240) = 0\), then \(x = -240\) [But the price of the watch cannot be negative] When \((x - 140) = 0\), then \(x = 140\) ∴ The cost price of the watch was 140 rupees, and selling it for 336 rupees gave him a profit of 140%.
Let the watch be purchased for \(x\) rupees. According to the question, selling the watch for 336 rupees gave him a profit of \(x\%\). ∴ A profit of \(x\) rupees on a cost price of 100 rupees means: On \(x\) rupees, the profit = \(\cfrac{x}{100} \times x = \cfrac{x^2}{100}\) rupees ∴ According to the question: \[ x + \cfrac{x^2}{100} = 336 \] \[ \cfrac{100x + x^2}{100} = 336 \] \[ 100x + x^2 = 33600 \] \[ x^2 + 100x - 33600 = 0 \] \[ x^2 + 240x - 140x - 33600 = 0 \] \[ x(x + 240) - 140(x + 240) = 0 \] \[ (x + 240)(x - 140) = 0 \] ∴ Either \((x + 240) = 0\) or \((x - 140) = 0\) When \((x + 240) = 0\), then \(x = -240\) [But the price of the watch cannot be negative] When \((x - 140) = 0\), then \(x = 140\) ∴ The cost price of the watch was 140 rupees, and selling it for 336 rupees gave him a profit of 140%.