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Question
Divide Rs. 20304 into two parts such that if one part is invested in 9% Rs. 50 shares at 8% premium and the other part is invested in 8% Rs. 25 shares at 8% discount, then the annual incomes from both the investment are equal
Solution
Total amount = Rs 20304
Let amount invested in 9% Rs 50 at 8%
premium = x
Then amount invested in 8% Rs 25 at 8%
Discount = 20304 – x
Income from both investments are equal Now income from first type of shares
= `(x xx 9)/(100 + 8) = (9x)/(108) = x/(12)`
Income from second type of shares
= `((20304 - x) xx 8)/(100 - 8)`
= `((20304 - x) xx 8)/(92)`
= `(2(20304 - x))/(23)`
∵ In both cases, annual income is same
∴ `x/(12) = (2(20304 - x))/(23)`
⇒ 23x = 24(20304 - x) ...(By cross multiplication)
⇒ 23x = 24 x 20304 - 24x
⇒ 23x + 24x = 24 x 20304
⇒ 47x = 24 x 20304
∴ x = `(24 xx 20304)/(47)` = 10368
∴ Amount invested in first kind of shares
= ₹10368
and in second kind of shares
= ₹20304 - ₹10368
= ₹9936.
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