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Question
A man invests Rs. 6750, partly in shares of 6% at Rs. 140 and partly in shares of 5% at Rs. 125. If his total income is Rs. 280, how much has he invested in each?
Solution
Let the investment in first case = x
Then investment in second case = (6750 – x)
In first case, the dividend
= `x xx (6)/(140) = "Rs." (3)/(70)x`
and dividend in second case
= `(6750 - x) xx (5)/(125) = "RS."(750 - x)/(25)`
∴ Total divided = `(3)/(70)x + (6750 - x)/(25)`
∴ `(3)/(70)x + (6750 - x)/(25)` = 280
⇒ 15x + 14(6750 - x) = 280 x 350 ...(L.C.M. = 350)
⇒ 15x + 14 x 6750 - 14x = 280 x 350
⇒ x = 280 x 350 - 14 x 6750
= 98000 - 94500 = Rs. 3500
∴ Investment in first case = Rs. 3500
and investment in second case
= 6750 - 3500
= Rs. 3250.
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