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 answer is 21%.

To solve this problem cleanly, let's assume A's total monthly income is 100 units (this makes percentages easy to track).

Step 1: Calculate the amount spent on Rent

A spends 30% of his income on rent.

\text{Rent}=30\%\times 100=30\text{units}

\text{Remaining after Rent}=100-30=70\text{units}

Step 2: Calculate the amount spent on Groceries

A spends 25% of the remaining amount (i.e., 25% of 70) on groceries.

\text{Groceries}=25\%\times 70=\frac{25}{100}\times 70=17.5\text{units}

\text{Remaining after Groceries}=70-17.5=52.5\text{units}

Step 3: Split the remaining amount between Entertainment and Savings

The remaining 52.5 units are divided between entertainment and savings in the ratio 2 : 3.

Total ratio parts = 2 + 3 = 5 parts

Entertainment gets 2 out of every 5 parts:

\text{Entertainment}=\frac{2}{5}\times 52.5=21\text{units}

Step 4: Express Entertainment as a percentage of total income

Since we assumed total income = 100 units, the entertainment amount directly gives us the percentage:

\text{Entertainment \%}=\frac{21}{100}\times 100=21\%

Quick Verification:

Rent = 30 units
Groceries = 17.5 units
Entertainment = 21 units
Savings = \frac{3}{5}\times 52.5=31.5 units
Total = 30 + 17.5 + 21 + 31.5 = 100 ✓

Therefore, 21% of A's monthly income is spent on entertainment.