A shopkeeper marks his products 50% above the cost price and allows a discount of 20% on the marked price. He also gives an additional cash discount of ₹120 and still makes a profit of 16% on cost. What is the cost price of the product?

The correct answer is ₹3,000.

Let us solve this problem step-by-step by defining the variables and following the given financial conditions.

Step 1: Define the Cost Price (CP)

Let the Cost Price of the product be $\mathrm{CP}=x$.

Step 2: Calculate the Marked Price (MP)

The shopkeeper marks his products 50% above the cost price.

$\mathrm{MP}=x+0.50x=1.5x$

Step 3: Calculate the Price after the first discount

A discount of 20% is allowed on the marked price.

$\text{Price after 20\% discount}=1.5x\times (1-0.20)=1.5x\times 0.80=1.2x$

Step 4: Calculate the Final Selling Price (SP)

An additional cash discount of ₹120 is given.

$\mathrm{SP}=1.2x-120$

Step 5: Relate Selling Price to Profit Percentage

The shopkeeper still makes a profit of 16% on the cost price.

$\mathrm{SP}=\mathrm{CP}\times (1+0.16)=1.16x$

Step 6: Solve for x (Cost Price)

Equating the two expressions for the Selling Price ($\mathrm{SP}$):

$1.2x-120=1.16x$

$1.20x-1.16x=120$

$0.04x=120$

$x=\frac{120}{0.04}$

$x=3000$

Therefore, the cost price of the product is ₹3,000.