A shop keeper sold an electric blender at a loss of 3$$\frac{1}{2}$$​%. Had he sold it for ₹172.5 more, he would have gained 8%. To gain 13%, he should sell it for:

Correct option is D

Given:

The shopkeeper sold the electric blender at a loss of 3.5%.

If the shopkeeper had sold the blender for ₹172.5 more, he would have gained 8%.

We need to find the price at which the shopkeeper should sell the blender to gain 13%.

Formula Used:

Loss $$= \frac{\text{Loss \%}}{100} \times \text{Cost Price (CP)}$$​​

Gain = $$\frac{\text{Gain \%}}{100} \times \text{Cost Price (CP)}$$​​

SP = CP - Loss

SP = CP + Gain

Solution:

Let the Cost Price be x.

The shopkeeper sold the blender at a 3.5% loss, so the selling price $$SP_1$$​ is:

​$$SP_1 = x - 0.035x = 0.965x$$​​

Selling Price with a gain of 8%.

If the shopkeeper had sold the blender for ₹172.5 more, the selling price would have been:

​$$SP_2 = SP_1 + 172.5 = 0.965x + 172.5$$​

This selling price represents an 8% gain, so:

​$$SP_2 = x + 0.08x = 1.08x$$​​

We now have the equation:

0.965x + 172.5 = 1.08x

172.5 = 1.08x - 0.965x

172.5 = 0.115x

x =$$\frac{172.5}{0.115} = 1500$$​

So, the cost price of the blender is ₹1500.

Selling Price for a 13% gain.

To gain 13%, the selling price $$SP_3$$​ should be:

​$$SP_3 = x + 0.13x = 1.13x$$​​

​$$SP_3 = 1.13 \times 1500 = 1695$$​
The shopkeeper should sell the blender for ₹1695 to gain 13%.

Alternate Method: 
Difference in SP = (Gain% + Loss%) / 100 × CP
​$$172.5 = \left(\frac{11.5}{100}\right) \times \text{CP} \\\Rightarrow \text{CP} = \frac{172.5 \times 100}{11.5} = 1500$$​​
SP at 13% gain = 1500 + 13% of 1500 = 1500 + 195 = ₹1695
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