A toy is sold for ₹$580.80$ after giving two successive discounts, each of $x\%$. If the marked price of the article is ₹$750$, then what is the value of $x$?

Given:Marked Price ($\text{MP}$) = ₹$750$ Selling Price ($\text{SP}$) = ₹$580.80$ Two successive discounts of $x\%$ each are applied.The relation between $\text{MP}$ and $\text{SP}$ with two equal successive discounts is:
$$\text{SP}=\text{MP}\times {\left(1-\frac{x}{100}\right)}^2$$
Substitute the given values:
$$580.80=750\times {\left(1-\frac{x}{100}\right)}^2$$
$${\left(1-\frac{x}{100}\right)}^2=\frac{580.80}{750}$$
$${\left(1-\frac{x}{100}\right)}^2=\frac{5808}{7500}$$
Simplify the fraction by dividing both numerator and denominator by 3:
$${\left(1-\frac{x}{100}\right)}^2=\frac{1936}{2500}$$
Take the square root on both sides:
$$1-\frac{x}{100}=\sqrt{\frac{1936}{2500}}$$
We know that $\sqrt{1936}=44$ and $\sqrt{2500}=50$:
$$1-\frac{x}{100}=\frac{44}{50}$$
$$1-\frac{x}{100}=0.88$$
$$\frac{x}{100}=1-0.88$$
$$\frac{x}{100}=0.12$$
$$x=12$$