A man invested ₹20,000 in three shares in the ratio 2:3:5. The shares paid…
2023
A man invested ₹20,000 in three shares in the ratio 2:3:5. The shares paid dividends of 10%, 30%, and 20%, respectively, on the investments during the year. Find his total dividend income.
Answer: A. ₹ 4200 — ConceptWhen a total amount T is divided in the ratio a:b:c, the three parts are T×a/(a+b+c), T×b/(a+b+c), and T×c/(a+b+c). Income at rate r% on a part is…
- A.
₹ 4200
- B.
₹4500
- C.
₹4800
- D.
₹5000
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Show answer & explanation
Correct answer: A
Concept
When a total amount T is divided in the ratio a:b:c, the three parts are T×a/(a+b+c), T×b/(a+b+c), and T×c/(a+b+c). Income at rate r% on a part is part×r/100; the total income is the sum of the incomes from all parts.
Application
The sum of the ratio terms is 2+3+5=10.
The three investments are ₹20,000×2/10=₹4,000; ₹20,000×3/10=₹6,000; and ₹20,000×5/10=₹10,000.
Their dividends are ₹4,000×10/100=₹400; ₹6,000×30/100=₹1,800; and ₹10,000×20/100=₹2,000.
Therefore, the total dividend is ₹400+₹1,800+₹2,000=₹4,200.
Cross-check
The ratio-weighted average dividend rate is (2×10+3×30+5×20)/10=21%. Thus, 21% of ₹20,000 is ₹4,200, confirming the total.
Result
The total dividend income is ₹4,200.