Question : A trader sold a cycle at a loss of 10%. If the selling price had been increased by Rs. 200, there would have been a gain of 6%. The cost price of the cycle is:
Option 1: Rs. 1200
Option 2: Rs. 1205
Option 3: Rs. 1250
Option 4: Rs. 1275
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Correct Answer: Rs. 1250
Solution : Let the cost price of the cycle be Rs. $x$. Selling price when loss is $10$% $=\frac{100- \text {Loss percentage}}{100}$ × Cost price = $\frac{90x}{100}$ Selling Price when profit is $6$% $= \frac{100 + \text {Profit percentage}}{100}$ × Cost price = $\frac{106x}{100}$ Difference between the two selling prices $=\frac{106x}{100}-\frac{90x}{100} = \frac{16x}{100}$ So, $\frac{16x}{100} = 200$ ⇒ $x = \frac{20000}{16}$ $\therefore x$ = Rs. 1250 Hence, the correct answer is Rs. 1250.
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