Question : A man purchased 150 pens at the rate of Rs. 12 per pen. He sold 50 pens at a gain of 10%. The percentage gains at which he must sell the remaining pens so as to gain 15% on the whole outlay is:
Option 1: $21\frac{1}{2}\%$
Option 2:
$20\%$
Option 3:
$17\%$
Option 4: $17\frac{1}{2}\%$
Correct Answer: $17\frac{1}{2}\%$
Solution :
The cost price of each pen is Rs. 12.
The man purchased 150 pens.
The total cost price = 12 × 150 = Rs. 1,800
He sold 50 pens at a gain of 10%.
The selling price of these 50 pens = 12 × 50 × 1.10 = Rs. 660
The man wants to gain 15% on the whole outlay.
The total selling price for all 150 pens = 1800 × 1.15 = Rs. 2070
The selling price of the remaining 100 pens = 2070 – 660 = Rs. 1410
The selling price of each of the remaining pens = $\frac{1410}{100}$ = Rs. 14.1
The percentage gain on each of these pens
= $\frac{(14.10 - 12)}{ 12} \times 100 = 17\frac{1}{2}\%$
Hence, the correct answer is $17\frac{1}{2}\%$.
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