Question

Gagan invested 80% of his savings in 10% Rs. 100 shares at 20% premium and the rest of his savings in 20% Rs. 50 shares at 20% discount. If his incomes from these shares is Rs. 5,600, calculate:

1. his investment in shares on the whole.
2. the number of shares of first kind that he bought.
3. percentage return, on the shares bought, on the whole.

Answer 1

i. Let the total savings be Rs. x.

For 1^st part:

N.V of each share = Rs. 100

M.V of each share = `100 + 20/100 (100)` = Rs. 120

Number of shares bought = `(0.8x)/120`   ...(Investment = Rs. x)

Dividend on each share = 10% of 100 = Rs. 10   ...(Rate = 10%)

Total dividend = `10 xx (0.8x)/120 = Rs. (0.8x)/12`

For 2^nd part:

N.V of each share = Rs. 50

M.V of each share = `50 - 20/100 (50)` = Rs. 40

Number of shares bought = `(0.2x)/40`  ...(Investment = Rs. x)

Dividend on each share = 20% of 50 = Rs. 10  ...(Rate = 20%)

Total dividend = `10 xx (0.2x)/40 = (0.2x)/4`

Given that dividends (incomes) from both investments are Rs. 5,600

`\implies (0.8x)/12 + (0.2x)/4 = 5600`

`\implies (0.8x + 0.6x)/12 = 5600`

`\implies x = (5600 xx 12)/1.4`

`\implies` x = 48,000

Thus, his investment in shares on the whole is Rs. 48,000

ii. So, number of shares bought

= `(0.8x)/120`

= `(0.8 xx 48000)/120`

= Rs. 320

iii. The total dividend (return)

= `(0.8x)/12 + (0.2x)/4`

= `(0.8(48000))/12 + (0.2(48000))/4`

= 0.8 × 4000 + 0.2 × 12000

= Rs. 5,600

Percentage return = `5600/(48000) xx 100`

= `11 2/3`%