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Question
Varun invested 25%, 30%, and 20% of his savings in buying shares of three different companies. ‘A’, ‘B’ and ‘C’ which declared dividends. 10%, 12% and 15% respectively. If his total income on account of dividends is Rs. 6370/-, find the amount he invested in buying shares of company ‘B’.
Solution
Let ‘T’ be Varun’s total savings.
∴ Investment of Varun in:
Company A = 25% of T = `25/100 xx "T" = "T"/4`,
Company B = 30% of T = `30/100 xx "T" = (3"T")/10` and
Company C = 20% of T = `20/100 xx "T" = ("T")/5`
Company A, B, and C declared dividends 10%, 12%, and 15% respectively.
∴ Dividend from company A = 10% of `("T")/4`
= `10/100 xx "T"/4 = "T"/40` ......(i)
Dividend from company B = 12% of `(3"T")/10`
= `12/100 xx (3"T")/10 = (9"T")/500` ......(ii)
Dividend from company C = 15% of `("T")/5`
= `15/100 xx "T"/5 = (3"T")/100` .....(iii)
Total income on account of dividend = ₹ 6,370 .
`"T"/40 + (9"T")/250 + (3"T")/100 = 6,370`....[From (i), (ii) and (iii)]
∴ `"T"((25 +36 + 30)/(1,000)) = 6,370`
∴ `(91"T")/(1,000) = 6,370`
∴ T = `(6,370 × 1000)/91 = 70,000`
∴ Amount invested by Varun in company B
= `(3"T")/10`
= `(3 xx 70,000)/10 = ₹ 21,000.`
∴ Varun invested ₹ 21,000 in company B.
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