A shopkeeper marks the price of a smartwatch 60% higher than its cost price and offers a discount of 15% on the marked price. If the profit earned by selling the smartwatch under this offer is Rs. 540, what is the difference between this profit and the profit earned if the smartwatch were sold at a 30% profit?

The correct option is 90.

Step-by-step Explanation:

Step 1: Represent Cost Price, Marked Price, and Selling Price in terms of a variable.

Let the Cost Price (CP) of the smartwatch be $100x$.

The shopkeeper marks the price 60% higher than the cost price:

$\text{Marked Price (MP)}=100x+60\%\text{of}100x=160x$

A discount of 15% is offered on the marked price:

$\text{Discount}=15\%\text{of}160x=0.15\times 160x=24x$

Therefore, the initial Selling Price (${\text{SP}}_1$) under this offer is:

${\text{SP}}_1=\text{MP}-\text{Discount}=160x-24x=136x$

Step 2: Calculate the value of $x$ using the given profit.

The profit earned under this offer (${\text{Profit}}_1$) is Rs. 540:

${\text{Profit}}_1={\text{SP}}_1-\text{CP}$

$540=136x-100x$

$36x=540$

$x=\frac{540}{36}=15$

Step 3: Calculate the profit if sold at a 30% profit.

If the smartwatch is sold at a 30% profit, the profit amount (${\text{Profit}}_2$) would be:

${\text{Profit}}_2=30\%\text{of CP}=30x$

${\text{Profit}}_2=30\times 15=\text{Rs.}450$

Step 4: Find the difference between the two profits.

$\text{Difference}={\text{Profit}}_1-{\text{Profit}}_2$

$\text{Difference}=540-450=\text{Rs.}90$

Hence, the difference between the two profits is 90.