An item with cost price of ₹120 is sold by P to R at a 12% profit. R earns a profit of ₹45.6on the item and sells it to Q. The profit of P would have been ____% if the item is soldby P to Q directly at the same selling price.

Correct option is B

Given:

Cost price of the item for P = ₹120

Profit made by P = 12%

Profit made by R = ₹45.6

Formula Used:

Selling Price = $$\text{Cost Price} \times (1 + \frac{\text{Profit Percentage}}{100})$$​​

Profit Percentage = $$\frac{\text{Profit}}{\text{Cost Price}} \times 100$$​​

Solution:

Selling price of P to R = $$120 \times \frac{112}{100}$$​ = ₹134.4

Selling price of R to Q is not given, but R's profit is ₹45.6.

R's selling price = Cost price of R + ₹45.6

Since R buys the item at ₹134.4 from P, Cost price for R = ₹134.4,

So, selling price of R to Q = ₹134.4 + ₹45.6 = ₹180

Profit percentage for P if sold directly to Q:

Selling price for Q = ₹180 

Profit made by P = ₹180 - ₹120 = ₹60

Profit percentage for P = $$\frac{60}{120} \times 100 = 50\%$$​​