A spends 30% of his monthly income on rent, 25% of the remaining on groceries, and the remaining amount on entertainment and savings in the ratio 2:3, respectively. What percentage of his income is spent on entertainment?

The correct option is 21%.

Let's break down the solution step-by-step to find the percentage of A's monthly income spent on entertainment:

Step 1: Assume a total monthly income.
To make calculations straightforward, let A's total monthly income be $I=100$ units.

Step 2: Calculate the expenditure on rent and find the remaining amount.
A spends 30% of his monthly income on rent.
Rent expenditure = $30\%\text{ of }100=30$ units.
Remaining income after rent = $100-30=70$ units.

Step 3: Calculate the expenditure on groceries.
A spends 25% of the remaining income on groceries.
Groceries expenditure = $25\%\text{ of }70=\frac{25}{100}\times 70=17.5$ units.
Remaining income after groceries = $70-17.5=52.5$ units.

Step 4: Divide the remaining amount between entertainment and savings.
The remaining amount (52.5 units) is divided between entertainment and savings in the ratio $2:3$.
Total parts in the ratio = $2+3=5$ parts.
The fraction of the remaining amount spent on entertainment is $\frac{2}{5}$.

Step 5: Calculate the amount spent on entertainment.
Entertainment expenditure = $\frac{2}{5}\times 52.5$ units.
Entertainment expenditure = $2\times 10.5=21$ units.

Step 6: Express the entertainment expenditure as a percentage of the total income.
Since the total monthly income was assumed to be 100 units, the 21 units spent on entertainment represents:
Percentage of income spent on entertainment = $\frac{21}{100}\times 100\%=21\%$.