1313\frac{1}{3} of the capital for 9 months and Y received 25" role="presentation">2525\frac{2}{5} of the profit. For how long was Y's money used in the business ?" /> 1313\frac{1}{3} of the capital for 9 months and Y received 25" role="presentation">2525\frac{2}{5} of the profit. For how long was Y's money used in the business ?" /> 1313\frac{1}{3} of the capital for 9 months and Y received 25" role="presentation">2525\frac{2}{5} of the profit. For how long was Y's money used in the business ?" />

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X and Y are partners in a business. X contributed $\frac{1}{3}$ $\frac{1}{3}$ of the capital for 9 months and Y received $\frac{2}{5}$ $\frac{2}{5}$ of the profit. For how long was Y's money used in the business ?

12 months
23 months
34 mo0nths
45 months

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let  the total profit be Rs . z \\ Then, \\ Y's share = Rs . \frac{2 z}{5} \\ X's share = Rs . (z - \frac{2 z}{5}) \\ = Rs . \frac{3 z}{5} \\ ∴ X : Y \\ = \frac{3 z}{5} : \frac{2 z}{5} \\ = 3 : 2 \end{aligned}

$\eqalign{ & {\text{Let the total profit be Rs}}{\text{.}}\,z \cr & {\text{Then,}} \cr & {\text{Y's share}} = {\text{Rs}}{\text{.}}\,\frac{{2z}}{5} \cr & {\text{X's share}} = {\text{Rs}}{\text{.}}\left( {z - \frac{{2z}}{5}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,\frac{{3z}}{5} \cr & \therefore {\text{X}}:{\text{Y}} \cr & = \frac{{3z}}{5}:\frac{{2z}}{5} \cr & = 3:2 \cr}$
Let the total capital be Rs. x and
Suppose Y's money was used for y months
Then,

\begin{aligned} \Rightarrow \frac{\frac{1}{3} x \times 9}{\frac{2}{3} x \times y} = \frac{3}{2} \\ \Rightarrow 18 x = 6 x y \\ \Rightarrow y = 3 \end{aligned}

$\eqalign{ & \Rightarrow \frac{{\frac{1}{3}x \times 9}}{{\frac{2}{3}x \times y}} = \frac{3}{2} \cr & \Rightarrow 18x = 6xy \cr & \Rightarrow y = 3 \cr}$
Hence, Y's money was used for 3 months.

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of the capital for 9 months and Y received

\frac{2}{5}

$\frac{2}{5}$ of the profit. For how long was Y's money used in the business ?", "text": "X and Y are partners in a business. X contributed

\frac{1}{3}

$\frac{1}{3}$ of the capital for 9 months and Y received

\frac{2}{5}

$\frac{2}{5}$ of the profit. For how long was Y's money used in the business ?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Let  the total profit be Rs . z \\ Then, \\ Y's share = Rs . \frac{2 z}{5} \\ X's share = Rs . (z - \frac{2 z}{5}) \\ = Rs . \frac{3 z}{5} \\ ∴ X : Y \\ = \frac{3 z}{5} : \frac{2 z}{5} \\ = 3 : 2 \end{aligned}

$\eqalign{ & {\text{Let the total profit be Rs}}{\text{.}}\,z \cr & {\text{Then,}} \cr & {\text{Y's share}} = {\text{Rs}}{\text{.}}\,\frac{{2z}}{5} \cr & {\text{X's share}} = {\text{Rs}}{\text{.}}\left( {z - \frac{{2z}}{5}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,\frac{{3z}}{5} \cr & \therefore {\text{X}}:{\text{Y}} \cr & = \frac{{3z}}{5}:\frac{{2z}}{5} \cr & = 3:2 \cr}$
Let the total capital be Rs. x and
Suppose Y's money was used for y months
Then,

\begin{aligned} \Rightarrow \frac{\frac{1}{3} x \times 9}{\frac{2}{3} x \times y} = \frac{3}{2} \\ \Rightarrow 18 x = 6 x y \\ \Rightarrow y = 3 \end{aligned}

$\eqalign{ & \Rightarrow \frac{{\frac{1}{3}x \times 9}}{{\frac{2}{3}x \times y}} = \frac{3}{2} \cr & \Rightarrow 18x = 6xy \cr & \Rightarrow y = 3 \cr}$
Hence, Y's money was used for 3 months. ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Let  the total profit be Rs . z \\ Then, \\ Y's share = Rs . \frac{2 z}{5} \\ X's share = Rs . (z - \frac{2 z}{5}) \\ = Rs . \frac{3 z}{5} \\ ∴ X : Y \\ = \frac{3 z}{5} : \frac{2 z}{5} \\ = 3 : 2 \end{aligned}

$\eqalign{ & {\text{Let the total profit be Rs}}{\text{.}}\,z \cr & {\text{Then,}} \cr & {\text{Y's share}} = {\text{Rs}}{\text{.}}\,\frac{{2z}}{5} \cr & {\text{X's share}} = {\text{Rs}}{\text{.}}\left( {z - \frac{{2z}}{5}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,\frac{{3z}}{5} \cr & \therefore {\text{X}}:{\text{Y}} \cr & = \frac{{3z}}{5}:\frac{{2z}}{5} \cr & = 3:2 \cr}$
Let the total capital be Rs. x and
Suppose Y's money was used for y months
Then,

\begin{aligned} \Rightarrow \frac{\frac{1}{3} x \times 9}{\frac{2}{3} x \times y} = \frac{3}{2} \\ \Rightarrow 18 x = 6 x y \\ \Rightarrow y = 3 \end{aligned}

$\eqalign{ & \Rightarrow \frac{{\frac{1}{3}x \times 9}}{{\frac{2}{3}x \times y}} = \frac{3}{2} \cr & \Rightarrow 18x = 6xy \cr & \Rightarrow y = 3 \cr}$
Hence, Y's money was used for 3 months. ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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