Number of preferential shares = 50,000
Number of ordinary shares = 2500
Total dividend = Total profit - Amount kept in reserve - Depreciation amount
= 1,60,000 - 20,000 - 10,000 = 1,30,000
Income from preferential shares
\(=50,000 \times 10 \times \frac{16}{100} \)
= 80,000
\(\therefore\) Income from ordinary shares
=1,30,000 - 80,000 = 50,000
Let x % be the rate of dividend for ordinary shares
\(50,000 =2500 \times 10 \times \frac{x}{100} \)
\(x =\frac{50,000}{250}=20 \%\)

(i) For Company A
Investment = Rs.27,000
M.V. = Rs.100
Number of shares  \(=\frac { 27000 }{ 100 } =270\)
(ii) For B
Investment = Rs.27,000

M.V.= Rs.100 + 25 = Rs.125
Number of shares \( =\cfrac { 27000 }{ 125 } =216\)
(iii) For C
M.V.= Rs.100-10 = Rs.90
Number of shares \(=\frac { 27000 }{ 90 } =300\)
(iv) For D
M.V. \(=50+\frac{20}{100} \times 50=50+10=60\)
Number of shares \(=\frac{27,000}{60}=450\)

a = Rs. 250, P = Rs. 6390, i = \(\frac { 6 }{ 1200 } \) = 0.05
P = \(\frac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
6390 = \(\frac { 250 }{6/1200 } \left[ \left( 1.005 \right) ^{ n }-1 \right] \)
6390 = 50,000[(1.005)ⁿ-1]
0.1278 + 1 = (1.005)ⁿ
1.1278 = (1.005)ⁿ
Taking logarithm on the boths sides log 1.1278 = n log 1.005
n = \(\cfrac { log\quad 1.1278 }{ log\quad 1.005 } =\cfrac { 0.0523 }{ 0.0022 } \)
n = 23.77 months
\(\Rightarrow\) n = 24 months
It will take 24 months for the deposit to amount to at least Rs. 6390

Let the number of shares be x.
Market value of 1 share = 100 - 10 = 90
Market value of x shares = 90x
Income from 10% discount shares
If Investment = 33, Income = 15
If Investment = 90x, Income  \(=\cfrac { 15 \times90x }{ 33 } \)   
Income from 10% premium shares
= \(\cfrac { 110x }{ 33 } \times 15\) 
\(\cfrac { 110x }{ 33 } \times 15-\cfrac { 90x }{ 33 } \times 15=450\)
\(\cfrac { 15x }{ 33 } {( 110 - 90) } =450\)
x = \(\cfrac { 450\times 33 }{ 15\times 20 } \) = 49.5~50 shares

Number of shares = \(\frac { 4500 }{ 10 } \) = 450
Annual income = No.of shares x F.V x Rate of dividend
= 450 x 10 x \(\frac { 2 }{ 100 } \) = Rs. 540
S.P of 450 shares = 450 x 23 = Rs. 10,350   
Number of shares bought \(=\frac { 10,350 }{ 18 } =575\)
Income = \(575 \times 25\times \frac { 10 }{ 100 } =Rs.1437.50\) 
Change in his income = 1437.50 - 540 
= Rs. 897.50