Mohan sold two same tables for ₹ 57120 each . On one he gains 15% and on other he loses 15%. Find his overall gain or loss percent.

Correct option is A

Given:
Mohan sold two tables for ₹57,120 each.
On one table, he gains 15%.

On the other table, he loses 15%.
Formula Used:

Selling Price (SP) = Cost Price (CP) + Gain.

Selling Price (SP) = Cost Price (CP) - Loss.

$$\text{Overall Loss Percentage} = \left( \frac{\text{Gain Percentage} \times \text{Loss Percentage}}{100} \right).$$

Solution:

Let the cost price of each table be x .
​$$x = \frac{57120}{1.15} = 49669.57$$​​

​$$\text{SP}_1 = x + 0.15x = 1.15x.$$​​
1.15x = 57120 

x = $$\frac{57120}{1.15}=49669.57$$

SP₂= x - 0.15x =0.85x
0.85x = 57120 
​$$x = \frac{57120}{0.85} = 67200$$​​
$$\text{Total CP} = x + x = 49669.57 + 67200 = 116869.57$$​

​$$\text{Total SP} = 57120 + 57120 = 114240$$​​
​$$\text{Loss} = \text{Total CP} - \text{Total SP} = 116869.57 - 114240 = 2629.57 .$$​
​$$\text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 = \left( \frac{2629.57}{116869.57} \right) \times 100 \approx 2.25\%.$$​​

Alternate Method:

Use the formula for overall gain or loss percentage when two items are sold at the same price with equal gain and loss percentages:
​$$\text{Overall Loss Percentage} = \left( \frac{\text{Gain Percentage} \times \text{Loss Percentage}}{100} \right).$$​​
​$$\text{Overall Loss Percentage} = \left( \frac{15 \times 15}{100} \right) = 2.25\%.$$​