12:13:1512:13:15\frac{1}{2}:\frac{1}{3}:\frac{1}{5} in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?" /> 12:13:1512:13:15\frac{1}{2}:\frac{1}{3}:\frac{1}{5} in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?" /> 12:13:1512:13:15\frac{1}{2}:\frac{1}{3}:\frac{1}{5} in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?" />

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A, B and C invested money in the ratio of $\frac{1}{2} : \frac{1}{3} : \frac{1}{5}$ $\frac{1}{2}:\frac{1}{3}:\frac{1}{5}$ in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?

1Rs. 20000, Rs. 25000, Rs. 18000
2Rs. 15500, Rs. 27200, Rs. 20450
3Rs. 22500, Rs. 6750, Rs. 5400
4Rs. 10350, Rs. 21540, Rs. 12050

Answer:- 1

Explanation:-

Solution:

Ratio of capital invested by

A, B and C = 15 : 10 : 6

${\text{A, B and C}} = 15:10:6$
Total capital invested by A in 1 year

\begin{aligned} = 15 x \times 4 + 30 x \times 8 \\ = 300 x \end{aligned}

$\eqalign{ & = 15x \times 4 + 30x \times 8 \cr & = 300x \cr}$
Total capital invested by B in 1 year

\begin{aligned} = 10 x \times 6 + 5 x \times 6 \\ = 90 x \end{aligned}

$\eqalign{ & = 10x \times 6 + 5x \times 6 \cr & = 90x \cr}$
Total capital invested by C in 1 year

\begin{aligned} = 6 x \times 12 \\ = 72 x \end{aligned}

$\eqalign{ & = 6x \times 12 \cr & = 72x \cr}$
Ratio of profits:

A	:	B	:	C
300x	:	90x	:	72x
50x	:	15x	:	12x

According to the question,

\Leftrightarrow (50 x + 15 x + 12 x)

$\Leftrightarrow \left( {50x + 15x + 12x} \right)$ =

Rs . 34650

${\text{Rs}}{\text{. 34650}}$

\begin{aligned} \Leftrightarrow 77 x = Rs . 34650 \\ \Leftrightarrow x = Rs . \frac{34650}{77} \\ \Leftrightarrow x = Rs . 450 \\ Profit of A = Rs . 450 \times 50 \\ = Rs . 22500 \\ Profit of B = Rs . 450 \times 15 \\ = Rs . 6750 \\ Profit of C = Rs . 450 \times 12 \\ = Rs . 5400 \end{aligned}

$\eqalign{ & \Leftrightarrow 77x = {\text{Rs}}.{\text{ }}34650 \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}\frac{{34650}}{{77}} \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}450 \cr & {\text{Profit of A}} = {\text{Rs}}{\text{. }}450 \times 50 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 22500}} \cr & {\text{Profit of B}} = {\text{Rs}}{\text{. }}450 \times 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 6750}} \cr & {\text{Profit of C}} = {\text{Rs}}{\text{. }}450 \times 12 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 5400}} \cr}$

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in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?", "text": "A, B and C invested money in the ratio of

\frac{1}{2} : \frac{1}{3} : \frac{1}{5}

$\frac{1}{2}:\frac{1}{3}:\frac{1}{5}$ in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

Ratio of capital invested by

A, B and C = 15 : 10 : 6

${\text{A, B and C}} = 15:10:6$
Total capital invested by A in 1 year

\begin{aligned} = 15 x \times 4 + 30 x \times 8 \\ = 300 x \end{aligned}

$\eqalign{ & = 15x \times 4 + 30x \times 8 \cr & = 300x \cr}$
Total capital invested by B in 1 year

\begin{aligned} = 10 x \times 6 + 5 x \times 6 \\ = 90 x \end{aligned}

$\eqalign{ & = 10x \times 6 + 5x \times 6 \cr & = 90x \cr}$
Total capital invested by C in 1 year

\begin{aligned} = 6 x \times 12 \\ = 72 x \end{aligned}

$\eqalign{ & = 6x \times 12 \cr & = 72x \cr}$
Ratio of profits:

A	:	B	:	C
300x	:	90x	:	72x
50x	:	15x	:	12x

According to the question,

\Leftrightarrow (50 x + 15 x + 12 x)

$\Leftrightarrow \left( {50x + 15x + 12x} \right)$ =

Rs . 34650

${\text{Rs}}{\text{. 34650}}$

\begin{aligned} \Leftrightarrow 77 x = Rs . 34650 \\ \Leftrightarrow x = Rs . \frac{34650}{77} \\ \Leftrightarrow x = Rs . 450 \\ Profit of A = Rs . 450 \times 50 \\ = Rs . 22500 \\ Profit of B = Rs . 450 \times 15 \\ = Rs . 6750 \\ Profit of C = Rs . 450 \times 12 \\ = Rs . 5400 \end{aligned}

$\eqalign{ & \Leftrightarrow 77x = {\text{Rs}}.{\text{ }}34650 \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}\frac{{34650}}{{77}} \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}450 \cr & {\text{Profit of A}} = {\text{Rs}}{\text{. }}450 \times 50 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 22500}} \cr & {\text{Profit of B}} = {\text{Rs}}{\text{. }}450 \times 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 6750}} \cr & {\text{Profit of C}} = {\text{Rs}}{\text{. }}450 \times 12 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 5400}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Ratio of capital invested by

A, B and C = 15 : 10 : 6

${\text{A, B and C}} = 15:10:6$
Total capital invested by A in 1 year

\begin{aligned} = 15 x \times 4 + 30 x \times 8 \\ = 300 x \end{aligned}

$\eqalign{ & = 15x \times 4 + 30x \times 8 \cr & = 300x \cr}$
Total capital invested by B in 1 year

\begin{aligned} = 10 x \times 6 + 5 x \times 6 \\ = 90 x \end{aligned}

$\eqalign{ & = 10x \times 6 + 5x \times 6 \cr & = 90x \cr}$
Total capital invested by C in 1 year

\begin{aligned} = 6 x \times 12 \\ = 72 x \end{aligned}

$\eqalign{ & = 6x \times 12 \cr & = 72x \cr}$
Ratio of profits:

A	:	B	:	C
300x	:	90x	:	72x
50x	:	15x	:	12x

According to the question,

\Leftrightarrow (50 x + 15 x + 12 x)

$\Leftrightarrow \left( {50x + 15x + 12x} \right)$ =

Rs . 34650

${\text{Rs}}{\text{. 34650}}$

\begin{aligned} \Leftrightarrow 77 x = Rs . 34650 \\ \Leftrightarrow x = Rs . \frac{34650}{77} \\ \Leftrightarrow x = Rs . 450 \\ Profit of A = Rs . 450 \times 50 \\ = Rs . 22500 \\ Profit of B = Rs . 450 \times 15 \\ = Rs . 6750 \\ Profit of C = Rs . 450 \times 12 \\ = Rs . 5400 \end{aligned}

$\eqalign{ & \Leftrightarrow 77x = {\text{Rs}}.{\text{ }}34650 \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}\frac{{34650}}{{77}} \cr & \Leftrightarrow x = {\text{Rs}}{\text{. }}450 \cr & {\text{Profit of A}} = {\text{Rs}}{\text{. }}450 \times 50 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 22500}} \cr & {\text{Profit of B}} = {\text{Rs}}{\text{. }}450 \times 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 6750}} \cr & {\text{Profit of C}} = {\text{Rs}}{\text{. }}450 \times 12 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 5400}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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