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A and B started a business by investing Rs. 2400 and Rs. 3600 respectively. At the end 4th months from the stat of the business, C joined with Rs. X. After 8 months from the start of the business, B withdrew Rs. 600. If C's share is Rs. 8000 in the annual profit of Rs. 22500, what was the amount C invested in the business ?

1Rs. 7200
2Rs. 5800
3Rs. 4000
4Rs. 4800

Answer:- 1

Explanation:-

Solution:

A invests Rs. 2400 for 12 months
B invests Rs. 3600 for 8 months
And Rs. 3000 for 4 months
C invests Rs. X for 8 months
Ratio of profit of A, B and C

\Rightarrow Profit of A

$\Rightarrow {\text{Profit of A}}$ :

Profit of B

${\text{Profit of B}}$ :

Profit of C

${\text{Profit of C}}$

\Rightarrow 2400 \times 12

$\Rightarrow {\text{2400}} \times {\text{12}}$ :

(3600 \times 8)

$\left( {3600 \times 8} \right)$ +

(3000 \times 4)

$\left( {3000 \times 4} \right)$ :

X \times 8

${\text{X}} \times 8$

\begin{aligned} \Rightarrow 28800 : 40800 : 8 X \\ \Rightarrow 3600 : 5100 : X \end{aligned}

$\eqalign{ & \Rightarrow 28800:40800:8{\text{X}} \cr & \Rightarrow 3600:5100:{\text{X}} \cr}$
Given profit of C = Rs. 8000
And total profit of A, B and C = Rs. 22500

\begin{aligned} ∴ \frac{X \times 22500}{3600 + 5100 + X} = 8000 \\ \Rightarrow \frac{X \times 22500}{8700 + X} = 8000 \end{aligned}

$\eqalign{ & \therefore \frac{{{\text{X}} \times 22500}}{{3600 + 5100 + {\text{X}}}} = 8000 \cr & \Rightarrow \frac{{{\text{X}} \times 22500}}{{8700 + {\text{X}}}} = 8000 \cr}$

\Rightarrow 22500 X

$\Rightarrow 22500{\text{X}}$ =

69600000

$69600000$ +

8000 X

$8000{\text{X}}$

\begin{aligned} \Rightarrow 14500 X = 69600000 \\ \Rightarrow X = Rs . 4800 \end{aligned}

$\eqalign{ & \Rightarrow 14500{\text{X}} = 69600000 \cr & \Rightarrow {\text{X}} = {\text{Rs}}.\,4800 \cr}$

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:

Profit of B

${\text{Profit of B}}$ :

Profit of C

${\text{Profit of C}}$

\Rightarrow 2400 \times 12

$\Rightarrow {\text{2400}} \times {\text{12}}$ :

(3600 \times 8)

$\left( {3600 \times 8} \right)$ +

(3000 \times 4)

$\left( {3000 \times 4} \right)$ :

X \times 8

${\text{X}} \times 8$

\begin{aligned} \Rightarrow 28800 : 40800 : 8 X \\ \Rightarrow 3600 : 5100 : X \end{aligned}

$\eqalign{ & \Rightarrow 28800:40800:8{\text{X}} \cr & \Rightarrow 3600:5100:{\text{X}} \cr}$
Given profit of C = Rs. 8000
And total profit of A, B and C = Rs. 22500

\begin{aligned} ∴ \frac{X \times 22500}{3600 + 5100 + X} = 8000 \\ \Rightarrow \frac{X \times 22500}{8700 + X} = 8000 \end{aligned}

$\eqalign{ & \therefore \frac{{{\text{X}} \times 22500}}{{3600 + 5100 + {\text{X}}}} = 8000 \cr & \Rightarrow \frac{{{\text{X}} \times 22500}}{{8700 + {\text{X}}}} = 8000 \cr}$

\Rightarrow 22500 X

$\Rightarrow 22500{\text{X}}$ =

69600000

$69600000$ +

8000 X

$8000{\text{X}}$

\begin{aligned} \Rightarrow 14500 X = 69600000 \\ \Rightarrow X = Rs . 4800 \end{aligned}

$\eqalign{ & \Rightarrow 14500{\text{X}} = 69600000 \cr & \Rightarrow {\text{X}} = {\text{Rs}}.\,4800 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

A invests Rs. 2400 for 12 months
B invests Rs. 3600 for 8 months
And Rs. 3000 for 4 months
C invests Rs. X for 8 months
Ratio of profit of A, B and C

\Rightarrow Profit of A

$\Rightarrow {\text{Profit of A}}$ :

Profit of B

${\text{Profit of B}}$ :

Profit of C

${\text{Profit of C}}$

\Rightarrow 2400 \times 12

$\Rightarrow {\text{2400}} \times {\text{12}}$ :

(3600 \times 8)

$\left( {3600 \times 8} \right)$ +

(3000 \times 4)

$\left( {3000 \times 4} \right)$ :

X \times 8

${\text{X}} \times 8$

\begin{aligned} \Rightarrow 28800 : 40800 : 8 X \\ \Rightarrow 3600 : 5100 : X \end{aligned}

$\eqalign{ & \Rightarrow 28800:40800:8{\text{X}} \cr & \Rightarrow 3600:5100:{\text{X}} \cr}$
Given profit of C = Rs. 8000
And total profit of A, B and C = Rs. 22500

\begin{aligned} ∴ \frac{X \times 22500}{3600 + 5100 + X} = 8000 \\ \Rightarrow \frac{X \times 22500}{8700 + X} = 8000 \end{aligned}

$\eqalign{ & \therefore \frac{{{\text{X}} \times 22500}}{{3600 + 5100 + {\text{X}}}} = 8000 \cr & \Rightarrow \frac{{{\text{X}} \times 22500}}{{8700 + {\text{X}}}} = 8000 \cr}$

\Rightarrow 22500 X

$\Rightarrow 22500{\text{X}}$ =

69600000

$69600000$ +

8000 X

$8000{\text{X}}$

\begin{aligned} \Rightarrow 14500 X = 69600000 \\ \Rightarrow X = Rs . 4800 \end{aligned}

$\eqalign{ & \Rightarrow 14500{\text{X}} = 69600000 \cr & \Rightarrow {\text{X}} = {\text{Rs}}.\,4800 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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