An item costs ₹400. During a festival sale, a company offers a sale discount that offers x% off on its regular price along with a discount coupon of 10%. The price of the item after using both the sale discount and the discount coupon, is ₹216, What is the value of x?

The correct option is 40.

Let's break down the problem step-by-step to find the value of $x$:

1. Identify the given information:
- Regular price (original cost) of the item = ₹400
- First discount (sale discount) = $x\%$ off
- Second discount (coupon discount) = 10% off
- Final price of the item after applying both discounts = ₹216

2. Express the price after the first discount:
When a discount of $x\%$ is applied to the regular price of ₹400, the remaining price (price after sale discount) is given by:
$\text{Price after sale discount}=400\times \left(1-\frac{x}{100}\right)$

3. Express the price after the second discount:
Next, a discount coupon of 10% is applied to this intermediate price. This means the customer pays $100\%-10\%=90\%$ (or 0.9) of the price after the sale discount:
$\text{Final Price}=\left[400\times \left(1-\frac{x}{100}\right)\right]\times \left(1-\frac{10}{100}\right)$
$\text{Final Price}=400\times \left(1-\frac{x}{100}\right)\times 0.9$

4. Set up the equation and solve for $x$:
We are given that the final price is ₹216. Therefore:
$400\times \left(1-\frac{x}{100}\right)\times 0.9=216$

Multiply 400 by 0.9:
$360\times \left(1-\frac{x}{100}\right)=216$

Divide both sides by 360:

Simplify the fraction $\frac{216}{360}$ by dividing the numerator and the denominator by 72:
$1-\frac{x}{100}=0.6$

Rearrange the equation to solve for $\frac{x}{100}$:
$\frac{x}{100}=1-0.6$
$\frac{x}{100}=0.4$

Multiply both sides by 100:
$x=0.4\times 100$
$x=40$

Thus, the value of $x$ is 40.