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Question
A man invests ₹ 13,500 partly in 6% of ₹ 100 shares at ₹ 140 and the remaining in 5% of ₹ 100 shares at ₹ 125. If his total income is ₹ 560, how much has he invested in each?
Solution
Let the amount invested in 6% of ₹ 100 shares at ₹ 140 be x.
Then the amount invested in 5% of ₹ 100 shares at ₹ 125 is ₹ 13500 – x.
Income from 6% shares = Number of shares × Face value of a share × Rate of dividend
= `"x"/140 xx 100 xx 6/100`
= `(3"x")/70`
Income from 5% shares = Number of shares × Face value of a share × Rate of dividend
= `(13500 - "x")/125 xx 100 xx 5/100`
= `(13500 - "x")/25`
Given that the total income = ₹ 560
`(3"x")/70 + (13500 - "x")/25` = 560
`((3"x") xx 5 + (13500 - "x") xx 14)/350` = 560
`(15"x" + 13500 xx 14 - 14"x")/350` = 560
x + 13500 × 14 = 560 × 350
x = 196000 – 189000 = 7000
Amount invested at 6% stock = ₹ 7,000
Amount invested at 5% stock = ₹ 13500 – ₹ 7000 = ₹ 6500
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