Rajat invested ₹ 24,000 in 7% hundred rupee shares at 20% discount. After one year, he sold these shares at ₹ 75 each and invested the proceeds (including dividend of first year) in 18% twenty five rupee shares at 64% premium. Find :

(i) his gain or loss after one year.

(ii) his annual income from the second investment.

(iii) the percentage of increase in return on his original investment.

Given, investment = ₹ 24000, div % = 7%, N.V. = ₹ 100,

⇒ M.V. = N.V. - discount

⇒ M.V. = ₹ 100 - $\dfrac{20}{100} \times 100$ = ₹ 100 - ₹ 20 = ₹ 80.

(i) No. of shares = $\dfrac{\text{Investment}}{\text{M.V. of each share}} = \dfrac{₹ 24000}{₹ 80}$ = 300.

∴ Dividend on 1 share = 7% of ₹ 100 = ₹ 7

∴ Rajat's dividend for the first year = ₹ 7 × 300 = ₹ 2100.

Hence, Rajat gained ₹ 2100 in first year.

(ii) Since, each share is sold for ₹ 75

∴ Proceeds (including dividend) = 300 × ₹ 75 + ₹ 2100 = ₹ 22500 + ₹ 2100 = ₹ 24600.

N.V. of each share = ₹ 25

M.V. of each share = N.V. + 64% of N.V.

= ₹ 25 + $\dfrac{64}{100} \times 25$

= ₹ 25 + ₹ 16

= ₹ 41

Dividend = 18%

∴ No. of shares bought = $\dfrac{\text{Investment}}{\text{M.V. of each share}} = \dfrac{₹ 24600}{₹ 41}$ = 600.

Dividend on 1 share = 18% of ₹ 25 = $\dfrac{18 \times 25}{100}$ = ₹ 4.50

Annual dividend (income) from second investment = 600 × ₹ 4.50 = ₹ 2700.

Hence, annual dividend (income) from second investment = ₹ 2700.

(iii) Increase in return = ₹ 2700 - ₹ 2100 = ₹ 600.

Percentage increase in return (on original investment) = $\dfrac{600}{24000} \times 100 = \dfrac{100}{40}$ = 2.5 %.

Hence, percentage increase in return = 2.5 %.