Question

Divide Rs. 101520 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 50 shares at 8% premium, the annual incomes are equal.

Answer 1

Total investment = Rs. 101520
Let investment in first part = x
and in second part = (101520 – x)
Market value of first kind of shares = Rs. 100 – Rs. 8
= Rs. 92
and rate of dividend = 8%

∴ Dividend = `(x xx 8)/(92) = "Rs." (2x)/(23)`
Market value of second kind = (101520 - x)
Rate of dividend = 9%

and market value = `"Rs." (100 + 8)/(100) xx 50`

= `(108)/(100) xx 50`
= Rs. 54
∴ Dividend = `(101520 - x) xx (9)/(2 xx 54) = (101520 - x)/(12)`

∴ According to the sum `(2x)/(23) = (101520 - x)/(12)`
⇒ 24x = 101520 x 23 - 23x
⇒ 24x + 23x = 101520 x 23
⇒ 47x = 101520 x 23

∴ x = `(101520 xx 23)/(47)` = 49680
∴ Investment of first part = Rs. 49680
and in second part
= Rs. 101450 - Rs. 49680
= Rs. 51840.