Nirmal and Kapil started a business investing Rs. 9000 and Rs. 12000 respectively. After 6 months, Kapil withdrew half of his investment. If after a year, the total profit was Rs. 4600, what was Kapil’s share initially ?

Answer: Option D

Explanation:

A:B:C = 35000:45000:55000
= 7:9:11

Now we are having the ratio.
to get the share, first make total of above ratio.
then get each share.

\begin{aligned}
\text{A's Share} = 40500*\frac{7}{27} \\
= Rs&10500 \\

\text{B's Share} = 40500*\frac{9}{27} \\
= Rs&13500 \\

\text{B's Share} = 40500*\frac{11}{27} \\
= Rs&16500 \\

\end{aligned}

Answer: Option C

Explanation:

Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)
= 48 : 32 : 64
= 3 : 2 : 4

\begin{aligned}
\text{Kamal's share}= 4005 * \frac{2}{9}\\
= Rs 890
\end{aligned}

Answer: Option B

Explanation:

Let the total profit be Rs. Z

Bharti's share = (2/3)Z
Rahul's Share = Z-(2/3)Z = Z/3

Rahul:Bharti = Z/3:(2/3)Z = 1:2

Now let the total capital be Rs X, and Bharti capital was used for Y months
then, Rahul capital will be (1/4)X and Bharti capital wil be X-(1/4)X = 3X/4
\begin{aligned}
\frac{\frac{1}{4}X*15}{\frac{3}{4}X*Y}= \frac{1}{2} \\
Y = \frac{15*2}{3} = 10
\end{aligned}

So Bharti's money was used for 10 months

Answer: Option B

Explanation:

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively

Then, 14x : 8y : 7z = 5 : 7 : 8

Now, 14x/8x = 5/7
=> y = (49/20)x

14x/7z = 5/8

=> z = (16/5)x

=>x:y:z = x:(49/20)x:(16/5)x
= 20:49:64

Answer: Option C

Explanation:

A:B:C = (8000*6):(4000*8):(8000*8)
= 48:32:64
= 3:2:4

So B share = (2/9)*4005 = Rs 890