A shopkeeper kept the marked price of an item at ₹500. He sold it at a scheme discount of 10% and 20% and got a profit of 25%. What was the cost price of the item?

The correct answer is ₹288.

Step-by-Step Explanation:
Let us break down the solution into simple steps to find the cost price of the item.

1. Find the Selling Price (SP) after successive discounts:
The marked price (MP) of the item is given as:
MP = ₹500
The item is sold at two successive discounts of 10% and 20%.
Selling Price after the first discount of 10% is:
$\mathrm{Price\; after\; 1st\; discount}=500\times \left(1-\frac{10}{100}\right)=500\times 0.9=₹450$

Selling Price after the second discount of 20% on the reduced price is:
$\mathrm{Final\; Selling\; Price\; (SP)}=450\times \left(1-\frac{20}{100}\right)=450\times 0.8=₹360$

2. Determine the Cost Price (CP) using the profit percentage:
The shopkeeper makes a profit of 25% by selling the item at the final selling price of ₹360.
The relationship between Selling Price, Cost Price, and Profit Percentage is given by:
$\mathrm{SP}=\mathrm{CP}\times \left(1+\frac{\mathrm{Profit\%}}{100}\right)$

Substitute the known values into the equation:
$360=\mathrm{CP}\times \left(1+\frac{25}{100}\right)$

$360=\mathrm{CP}\times 1.25$

Now, solve for CP:
$\mathrm{CP}=\frac{360}{1.25}$

$\mathrm{CP}=\frac{360}{\frac{5}{4}}=360\times \frac{4}{5}$

$\mathrm{CP}=72\times 4=₹288$

Thus, the cost price of the item was ₹288.