Amit sold a mobile at a gain of 31%. Had it been sold at Rs. 294 more then the gain would have been 38%. Find the cost price of mobile.

Correct option is B

Given:

1. Amit sold a mobile at a gain of 31% .
2. If the mobile were sold for Rs. 294 more, the gain would have been 38% .
3. We need to find the cost price of the mobile.

Formula Used:

1. Selling price at a given gain:
​$$\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Gain \%}}{100}\right)$$​
2. For the second scenario:
​$$\text{Selling Price at 38\% gain} = \text{Selling Price at 31\% gain} + 294$$​

Solution:

1. Let the cost price of the mobile be C .
2. Selling price at 31% gain:
​$$\text{SP}_1 = C \times \left(1 + \frac{31}{100}\right) = C \times 1.31$$​
3. Selling price at 38% gain:
​$$\text{SP}_2 = C \times \left(1 + \frac{38}{100}\right) = C \times 1.38$$​
4. According to the problem:
​$$\text{SP}_2 = \text{SP}_1 + 294$$​
Substituting the values:
​$$C \times 1.38 = C \times 1.31 + 294$$​
5. Simplify the equation:
1.38C - 1.31C = 294
0.07C = 294
C = $$\frac{294}{0.07} = 4200$$​

Final Answer:

The cost price of the mobile is Rs. 4200

Correct Option: (B) Rs. 4200