A man invested 20,000 in some shares in the ratio 2:3:5 which pay dividends of 10%, 30% and 20%, respectively, on the investments in that year. Find the total dividend income of the man.

The correct answer is ₹4200.

The man invests a total of ₹20,000 across three types of shares in the ratio 2 : 3 : 5. The dividends earned are 10%, 30%, and 20% on each respective investment. We need to find the total dividend income.

Step 1: Find the total number of ratio parts.

Total parts = 2 + 3 + 5 = 10 parts

Step 2: Calculate the actual amount invested in each share.

Share 1 (ratio part = 2):
Investment₁ = $\frac{2}{10}$ × 20,000 = ₹4,000

Share 2 (ratio part = 3):
Investment₂ = $\frac{3}{10}$ × 20,000 = ₹6,000

Share 3 (ratio part = 5):
Investment₃ = $\frac{5}{10}$ × 20,000 = ₹10,000

Step 3: Calculate the dividend income from each share.

Dividend from Share 1 (10% on ₹4,000):
$\frac{10}{100}\times \mathrm{4,000}=$₹400

Dividend from Share 2 (30% on ₹6,000):
$\frac{30}{100}\times \mathrm{6,000}=$₹1,800

Dividend from Share 3 (20% on ₹10,000):
$\frac{20}{100}\times \mathrm{10,000}=$₹2,000

Step 4: Add all the dividend incomes to get the total.

Total Dividend = ₹400 + ₹1,800 + ₹2,000

$=$₹4,200

Therefore, the total dividend income of the man is ₹4,200, which confirms the correct answer.