Question

Mr. Gautam sold a certain number of ₹ 20 shares, paying 8% dividend, at ₹ 18 and invested the proceeds in ₹ 10 shares, paying 12% dividend, at 50% premium. If the change in his annual income is ₹ 120, find the number of shares sold by Mr. Gautam.

Answer 1

Let the number of shares Mr. Gautam sold be x.

For initial shares,

N.V. = ₹ 20

Rate of dividend = 8%

By formula,

Annual income (from first investment) = No. of shares × Rate of div. × N.V. of 1 share

= `x xx 8/100 xx 20`

= `(8x)/5`

S.P. of each share = ₹ 18.

Amount obtained on selling shares = S.P × No. of shares = ₹ 18x.

The proceeds he invested in ₹ 10 shares at ₹ 15, paying 12% dividend.

N.V. = ₹ 10

Premium = 50% of ₹ 10 

= `50/100 xx 10`

= 5

M.V. = N.V. + Premium

= ₹ 10 + 5

= ₹ 15

Number of shares = `"Total Investment"/"Market value if each share"`

= `(18x)/15`

= `(6x)/5`

The change in Mr. Gautam's annual income = ₹ 120

By formula,

Annual income (from second investment) = No. of shares × Rate of div. × N.V. of 1 share

= `(6x)/5 xx 12/100 xx 10`

= `(720x)/500`

= `(36x)/5`

Given, change in income = ₹ 120

`therefore (8x)/5 - (36x)/5 = 120`

⇒ `(40x - 36x)/25 = 120`

⇒ `(4x)/25 = 120`

⇒ `x = (120 xx 25)/4`

⇒ x = 750

Hence, Mr. Gautam sold 750 shares.