Question : A person having bought goods for Rs. 400 sells half of it at a gain of 5%. At what gain percentage must he sell the remainder, so as to gain 25% on the whole?
Option 1: 30%
Option 2: 25%
Option 3: 20%
Option 4: 45%
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Correct Answer: 45%
Solution :
Total cost price = Rs. 400
The cost price of the first half = Rs. 200
Profit = 5% of cost price = $\frac{5}{100}×200$ = Rs. 10
Selling price of first half = 200 + 10 = Rs. 210
Total profit = 25% of total cost price = $\frac{25}{100}×400$ = Rs. 100
Total selling price = 400 + 100 = Rs. 500
Selling price of second half = Total selling price – Selling price of first half
= Rs. 500 – Rs. 210 = Rs. 290
The cost price of the second half = Rs.200
⇒ Profit = Selling price – Cost price = Rs. 290 – Rs. 200 = Rs. 90
So, the profit percentage = $\frac{90}{200}×100$ = 45%
Hence, the correct answer is 45%.
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