Question : Ankita sold her watch at a 5% loss. If she had sold it for Rs. 300 more, she would have gained 5%. Find the selling price of the watch.
Option 1: Rs. 2,900
Option 2: Rs. 2,750
Option 3: Rs. 3,000
Option 4: Rs. 2,850
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Correct Answer: Rs. 2,850
Solution :
Ankita sold her watch at a 5% loss.
Here, SP = Selling price and CP = Cost price
Let the SP of the watch be $x$.
Then, CP $= \frac{100}{(100 - \text{Loss}\%)} \times SP =\frac{100}{(100- 5)} \times x = \frac{100}{95}x$
If she sold for 300 more, then $SP = 300 + x$
Then, gain = 5%
$CP =\frac{100}{(100 + P)} \times SP = \frac{100}{(100 +5)} \times (x + 300)$ = $\frac{100}{105}(300 + x)$
According to the question,
$\frac{100}{105}(300 + x) = \frac{100}{95}x$
$⇒\frac{(300 + x)}{x} = \frac{105}{95}$
$⇒95 \times (300 + x) = 105x$
$⇒28500 + 95x = 105x$
$⇒10x = 28500$
$\therefore x = 2850$
Hence, the correct answer is Rs. 2,850.
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