If goods be purchased for ₹450 and one third 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 B

Solution

We need to calculate the gain percentage at which the remainder of the goods must be sold to achieve an overall gain of 20%.

Step-by-Step Solution:

1. Given:

- Cost price of the goods: ₹450

- One-third of the goods is sold at a loss of 10%.

- Required overall gain: 20%.

2. Calculate the cost price of one-third of the goods:

​$$\text{Cost price of one-third} = \frac{1}{3} \times 450 = 150 \, \text{₹}$$​

3. Selling price of one-third of the goods (at 10% loss):

Selling price is given by:

​$$\text{Selling price} = \text{Cost price} \times (1 - \text{Loss Percentage})$$​

Substituting values:

​$$\text{Selling price of one-third} = 150 \times (1 - 0.10) = 150 \times 0.90 = 135 \, \text{₹}$$​

4. Calculate the required selling price for the whole transaction:

To achieve an overall gain of 20%, the total selling price must be:

​$$\text{Required total selling price} = \text{Cost price} \times (1 + \text{Gain Percentage})$$​

Substituting values:

​$$\text{Required total selling price} = 450 \times (1 + 0.20) = 450 \times 1.20 = 540 \, \text{₹}$$​

5. Calculate the selling price required for the remaining goods:

The remaining two-thirds of the goods must contribute:

​$$\text{Selling price of remainder} = \text{Required total selling price} - \text{Selling price of one-third}$$​

Substituting values:

​$$\text{Selling price of remainder} = 540 - 135 = 405 \, \text{₹}$$​

6. Cost price of the remaining goods:

The cost price of the remaining two-thirds of the goods is:

​$$\text{Cost price of remainder} = 450 - 150 = 300 \, \text{₹}$$​

7. Calculate the required gain percentage:

The gain percentage on the remainder is:

​$$\text{Gain Percentage} = \frac{\text{Selling price} - \text{Cost price}}{\text{Cost price}} \times 100$$​

Substituting values:

​$$\text{Gain Percentage} = \frac{405 - 300}{300} \times 100 = \frac{105}{300} \times 100 = 35\%$$​

Final Answer:

​$$\boxed{35\%}$$​