Question

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

Answer 1

Given:

Total investment = ₹ 101520

First Investment:

8% ₹ 100 shares at 8% discount

Market price = ₹ 100 − 8% of ₹ 100 = ₹ 92

Dividend per share = 8% of ₹ 100 = ₹ 8

Yield = `8/92 xx 100` = 8.6957%

Second Investment:

9% ₹ 50 shares at 8% premium

Market price = ₹ 50 + 8% of ₹ 50 = ₹ 54

Dividend per share = 9% of ₹ 50 = ₹ 4.50

Yield = `4.5/54 xx100 = 8.3333%`

Let the first part of the investment be ₹ x

= ₹ 101520 − x

`8/92 x = 4.5/54 (101520 - x)`

Multiply both sides by LCM of denominators (let’s use 4968):

(8⋅54) (x) = (4.5 ⋅ 92) (101520 − x)

⇒ 432x = 414(101520 − x)

432x = 41929280 − 414x

⇒ 432x + 414x = 41929280

⇒ 846x = 41929280

`=> x = 41929250/846`

= ₹ 49560

8% ₹100 shares at 8% discount = ₹ 49560

9% ₹50 shares at 8% premium = ₹ 101520 − ₹ 49560

= ₹ 51960