Profit's share of A and B $=\frac{(52,000\times 12)}{(39,000\times 8)}=2:1$

Let the profit be Rs. x, then B receives $25\%$ as commission for managing business, the remaining $75\%$ of the total profit x is shared between A and B in the ratio 2:1. Hence B will get ${\frac{1}{3}}^{rd}$ part of this in addition to his commission. Hence his total earning 

$=0.25x+\frac{1}{3}\times 0.75x$
$=0.5x=20,000$
$x=40,000$
So,the remaining profit goes to A,hence the profit of A is Rs.20,000.

Deepak was getting $10\%$ interest, $20\%$ of the interest i.e. $20\%$ of $10\%$ $(=2\%)$ was the tax which he had to pay, so the net interest rate (after tax)  $=10-2=8\%$

So, amount received by him after 3 years $=50000{(1+(\frac{8}{100}\left)\right)}^3=Rs.62985.6$

Hence option (5) 

2nd method:- By, pascal triangles for $n=3\&r=8\%$. Option (5).

Let the value of each installment is X, Total amount is P

$P=X(K+K^2+K^3+...................),WhereK=\frac{100}{100+r}$  Here only two years and r is $10\%$ then 

$P=X(K+K^2)$

$10000=x\{\frac{10}{11}+{\left(\frac{10}{11}\right)}^2\}$

X = 5761.9

Alternatively

$10,000(1.1{)}^2=x[1+\left(1.1\right)]$

x = 5761.9

The difference in the SI and CI for the second year $=\frac{P{r}^2}{{100}^2}=\mathrm{4500....................}\left(i\right)$
The difference in the SI and CI for the third year $=\frac{P{r}^2}{{100}^2}(3+\frac{r}{100})=\mathrm{14175...........}\left(ii\right)$
From the equation (i) and (ii).
$4500\times (3+\frac{r}{100})=14175$
$\frac{r}{100}=(\frac{14175}{4500}-3)$
$r=\frac{675}{45}.$ Now ,from equation  (i)
$P=\frac{4500}{r^2}\times {100}^2\Rightarrow P=\frac{4500}{675\times 675}\times {100}^2\times 45\times 45\Rightarrow P=2,00,000.$

Unless we know the amount we cannot derive the answer.

Hence option (e)

A can finish the work in 12 days.

He can finish $100\%$ of the work in 12 days.

In 1 day he can finish  $\left(\frac{100}{12}\right)\%=8.33\%$ of the work.

Similarly B can finish  $\left(\frac{100}{15}\right)\%=6.67\%$  of the work in 1 day.

When they both work together, they can finish  $(8.33+6.67)\%=15\%$  of the work in 1 day

So, to complete  $100\%$  of the work, they will take  $\left(\frac{100}{15}\right)e=6\left(\frac{2}{3}\right)$  days. Hence option (a).

2nd method:- Total work (W) = 12A = 15B ,  $B=\frac{4}{5}A$

n(A+B) = W = 12A or 15B (Here, we take 12A).

$n(A+B)=12A,n(A+\frac{4}{5}A),n=\frac{20}{3}=6\left(\frac{2}{3}\right)$days. Option (a).

Arun can finish  $100\%$  of work in 12 days he can finish  $\left(\frac{100}{12}\right)=8.33\%$  of the work in a day.

Ajit can finish  $100\%$  of work in 15 days he can finish  $\left(\frac{100}{15}\right)=6.67\%$   of the work in a day.

Amit can finish  $100\%$  of the work in 20 days he can finish $\left(\frac{100}{20}\right)=5\%$   of the work in a day.

So, if all three work together, then they can finish  $(8.33+6.67+5)\%=20\%$  of the work in a day.

So, they can complete the work in  $\left(\frac{100}{20}\right)$ = 5 days. Hence option (B).

2nd method:- W= 12A=15B=20C . 

$n(A+B+C)=12A,n(A+\frac{3}{4}A+\frac{3}{5}A)=12A,n=5days$.
Option (2).

In one day Ajit can do  $\left(\frac{100}{24}\right)\%$  of the work.

In one day Bharath can do  $\left(\frac{100}{30}\right)\%$   of the work.

Working together they can do  $\left(\frac{100}{24}\right)\%+\left(\frac{100}{30}\right)\%=7.5\%$  of the work in one day.

Now when Chandra joins them, they complete the work in 12 days Ajit, Bharath and Chandra together complete  $\left(\frac{100}{12}\right)\%$  of the work in a day.

Now, Ajit and Bharath do $7.5\%$ of the work in a day.

Ajit, Bharath and Chandra do  $\left(\frac{100}{12}\right)\%$   of the work in a day.

Chandra can do  $(\frac{100}{12}-7.5)\%=\left(\frac{10}{12}\right)\%$  of the work in a day.

So, to complete $100\%$ of the work, Chandra will take $\left[\frac{100}{\left(\frac{10}{12}\right)}\right]$= 120 days. Hence option (e).

2nd method:- In 12 days ajit completes $\frac{12}{24}$  i.e  $50\%$  and Bharat completes $\frac{12}{30}$ i.e  $40\%$ , then chandra completes $(100-90)=10\%$ work in 12 days. Then he will take 120 days to complete full work.

Let a, b and c be the % of the work done by A, B and C in one day respectively.

$A\&B$  can complete the work in 12 days   $a+b=\frac{100}{12}\%=8.33\%...\left(i\right)$

$B\&C$  can complete the work in 15 days   $b+c=\frac{100}{15}\%=6.67\%....\left(ii\right)$

$A\&C$  can complete the work in 20 days   $a+c=\frac{100}{20}\%=5\%....\left(iii\right)$

Adding (i), (ii) and (iii)

$2(a+b+c)=20\%\Rightarrow (a+b+c)=10\%$

So, working together they finish $10\%$  of work in a day. So, they can complete the work in 10 days.