Mahesh sold $$\tfrac{3}{4}$$​ of his stock at a gain of 20% and the remaining stock at a gain of 15%. Find the total gain percentage (approximate).

Correct option is A

Given:

Mahesh sold $$\frac{3}{4}$$​​ of his stock at 20% gain.

The remaining $$\frac{1}{4}$$​ of his stock at 15% gain.

We need to find the total gain percentage.

Concept Used:

$$\text{Total Gain \%} = \left( \frac{\text{Part 1 Gain} \times \text{Part 1 Fraction} + \text{Part 2 Gain} \times \text{Part 2 Fraction}}{\text{Total Fraction}} \right)$$

Solution:

$$\text{Total Gain \%} = \left( \frac{(20 \times \frac{3}{4}) + (15 \times \frac{1}{4})}{1} \right)\\= \frac{\frac{60}{4} + \frac{15}{4}}{1}$$​

= $$\left( \frac{60}{4} + \frac{15}{4} \right)$$​​

= $$\left( \frac{75}{4} \right)=18.75\%\approx 19\%$$

Option (B) is right.

Alternate Method:

Given:

Fraction of stock sold at 20% gain = $$\frac{3}{4}$$​​

Fraction of stock sold at 15% gain = 1 - $$\frac{3}{4}$$​= $$\frac{1}{4}$$​​

Concept Used:

Weighted average of the gain percentages.

Solution:

Calculate the weighted gain for the first part of the stock: $$\frac{3}{4} \times$$​ 20% = 15%

Calculate the weighted gain for the remaining stock: $$\frac{1}{4} \times$$​ 15% = 3.75%

Add the weighted gains together to find the total gain percentage: 15% + 3.75% = 18.75% $$\approx 19\%$$

Option (B) is right.​​

​

​