Let the number of shares be x.
Dividend = No.of shares x F.V x Rate percentage.
1620 =  \(x \times 20 \times \frac { 9 }{ 100 } \)
x = \(\frac { 1620\times 100 }{ 20\times 9 } \) = 900 shares

Face value = Rs. 100
Market value = Rs. (100 – 17 + 1) = Rs. 84
\(\therefore\) percentage of his income = \(\frac{(12\times 100)}{84}\)
= \(\frac{100}{7}=14\frac{2}{7}\)
\(\therefore\) % of Income = \(14\frac{2}{7}\%\)

Number of shares = 500
Face value of a share = Rs. 100
Discount = Rs. 14
Market value of a share = 100 – 14 = Rs. 86 (face value – discount)
Market value of 500 shares = Number of shares × market value of a share
= 500 × 86 = 43,000
Market value of 500 shares = Rs. 43,000

a = Rs.5000, i = \(\frac{10}{100}\) = 0.1, n = 12
\(A=\frac { a(1+i) }{ i } \left[ (1+i)^{ n }-1 \right] \)
\( \left[ \left( 1.1 \right) ^{ 12 }=3.1384 \right] \)
=\(\cfrac { 5000\left( 1.1 \right) }{ 0.1 } \left[ \left( 1.1 \right) ^{ 12 }-1 \right] \)
= 55,000 [3.1384 - 1]
= 55,000 [2.1384]
= Rs. 1,17,612

Here a = 36,000 ; n = 7 and i = 0.16
Now P = (1+ i) \(\frac{a}{i}[1-\frac{1}{(1+i)^n}]\)
= (1 + 0.16) \(\frac{36,000}{0.16}[1-\frac{1}{(1+0.16)^7}]\)
= \(\frac{1.160}{0.16}(36,000)[1-\frac{1}{(1+0.16)^7}]\)
= \(\frac{116\times 36000}{16}[1-\frac{1}{2.828}]\)
= \(\frac{116\times 36000}{16}[\frac{2,828-1}{2,828}]\)
= \(\frac{116\times36,000\times 1,828}{16\times 2,828}\)
= \(\frac{116\times 36,000\times 1828}{16\times 2828}≈ 1,68,709\)
\(\therefore\) P = Rs. 1,68,709

Shares of tea company
No.of shares = 2000
FV = Rs.10
MV = Rs.33
Rate of dividend = 25%
S.P of a share = Rs.33
S.P of 2000 shares = 2000 x 33 = Rs. 66,000
Shares of cotton textiles
Investment = Rs. 66,000
FV = Rs. 25
MV = Rs. 44
Dividend =15%
(i) Number of cotton textile shares
= \(\frac {\text{ Investment} }{ M.V } \)
=  \(\frac { 66,000 }{ 44 } =1500\)
(ii) Income from tea company shares
= 2000 x 10 x \(\frac { 25 }{ 100 } \) = Rs. 5000
Income from cotton textiles shares
= 1 500 x 25 x \(\frac { 15 }{ 100 } \) = Rs. 5625
Change in his dividend income = 5625 - 5000 = Rs. 625

Machine A:
Present value of out flow = Rs.15,000
a = Rs. 4000, i = 8/100 = 0.08, n = 4
P = \(\cfrac { a }{ i } =\left[ 1-\left( 1+i \right) ^{ -n } \right] \)
\(=\frac{4000}{0.08}\left[1-\frac{1}{(1.08)^4}\right]\)
= 50000 [1 -(1.08)^-4]
= 50000 [1 -0.7350] = Rs.13240
Present inflow is less then present outflow 
Net outflow = 15,000 - 13,250 = Rs.1750.
Machine B
a = 7000, i = 0.08, n = 7
P = \(\cfrac { a }{ i } \left[ 1-\left( 1+i \right) ^{ -n } \right] \)
= \(\cfrac { 7000 }{ 0.08 } \left[ 1-\left( 1.08 \right) ^{ -7 } \right] \)
= 87500(1-0.05835)
= 87500 x 0.4165 = Rs.36,443.75
Present inflow is more than present outflow.
Net inflow = 36,443.75 - 20000
= Rs. 16,443.75
Machine Ycan be purchased.

F.V. = Rs 10
Total face value of preference shares = Rs.1,00,000 \(\times\) 10 = Rs.10,00,000
Total face value of ordinary shares = Rs.50,000 \(\times\) 10 = Rs.5,00,000
Total dividend amount paid to shareholders = Rs.(3,20,000 – 40,000 – 20,000) = Rs.2,60,000
Dividend for preference shares = \(\frac{16}{100}\times 10,00,000\) = Rs 1,60,000
Dividend to ordinary shares = 2,60,000 – 1,60,000 = Rs 1,00,000
Dividend rate for ordinary share = \(\frac{Income}{investment}\times 100\%\)
Dividend = \(\frac{1,00,000}{5,00,000}\times 100\) = 20%.

Investment = 80, Income = 7
Investment = 100,
Income \(= \frac{ 7 \times 100}{80} = 8.75 \%\)

Amount = 200 x 50 = Rs. 10,000

Investment = 200 x 100 x \(\frac{8}{100}\)= Rs. 1600