If one fourth of the goods be sold at a loss of 15%. at what profit percent should the remaining goods be sold so as to gain 30% on the whole deed if the total goods are purchased of Rs. 600?
Solution
Correct Answer: Option E
According to the given information,
Cost Price of all goods = Rs. 600
⇒ Cost Price of 1/4th of goods = Rs. 150
∵ % loss on 1/4th of goods = 15%
⇒ \(\frac{{Cost\;Price - Selling\;Price}}{{Cost\;Price}} \times 100 = 15\)
⇒ 150 – Selling Price = 22.5
⇒ Selling Price of 1/4th of goods = 150 – 22.5 = Rs. 127.5
∵ Cost Price of total goods = Rs. 600
Total % gain required = 30%
\(\Rightarrow \frac{{Selling\;Price - Cost\;Price}}{{Cost\;Price}} \times 100 = 30\)
⇒ Selling Price of all goods – 600 = 180
⇒ Selling Price of all goods = Rs. 780
Required selling price for 3/4th of goods = 780 – 127.5 = Rs. 652.5
∵ Cost Price of 3/4th of goods = Rs. 450
∴ % Profit = \(\frac{{Selling\;Price - Cost\;Price}}{{Cost\;Price}} \times 100\; = \frac{{652.5 - 450}}{{450}}\; \times \;100\; = \;45\)
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