If goods are purchased at Rs. 450 and $$\frac{1}{3}$$ are sold at a loss of 10%, at what gain percentage should the remainder be sold so as to gain 20% on the whole transaction? ​

Correct option is D

Given:

Cost price of goods = Rs. 450

Fraction of goods sold =$$\frac{1}{3}$$​​

Loss on the sold goods = 10%

Desired gain on the whole transaction = 20%

Formula Used:

Selling Price at a Loss = Cost Price$$\times$$​(1 - Loss %)

Total Selling Price = Total Cost Price $$\times$$​(1 + Gain %)

Solution:

Selling price of goods sold at a loss (10%):
Goods sold = $$\frac{1}{3}$$​ of Rs. 450 = Rs. 150
Loss = 10% of Rs. 150 = Rs. 15
Selling price = Rs. 150 - Rs. 15 = Rs. 135

Remaining goods =$$\frac{2}{3}$$​of Rs. 450 = Rs. 300

Total selling price for 20% gain on the whole transaction:
Total cost price = Rs. 450
Required total selling price = Rs. 450$$\times$$​ (1 + 20%) = Rs. 450 $$\times$$​ 1.2 = Rs. 540

Total selling price required = Rs. 540
Selling price of goods already sold = Rs. 135
So, the selling price for the remaining goods = Rs. 540 - Rs. 135 = Rs. 405

Cost price of remaining goods = Rs. 300
Selling price of remaining goods = Rs. 405
Gain = Selling price - Cost price = Rs. 405 - Rs. 300 = Rs. 105
Gain percentage $$= \frac{105}{300} \times 100$$= 35% 

Exam Trick: ​