Question

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answer it...⬇️

X and Y started a business with investments of
₹5000 and ₹8000, respectively. After 6 months, Y withdrew an amount of ₹2000 from his investment and Z joined the business with an investment
of ₹6000. If the profit at the end of the year is₹9615, then what is the share of Y?​

Answer 1

AnswEr :

$\bullet\:\underline\textsf{Total Investment by X :}\\\longrightarrow\sf Amount \times Time\\\\\longrightarrow\sf Rs.\:5000 \times 12 \:months \\\\\longrightarrow\sf Rs.\:60000$

$\rule{120}{2}$

$\bullet\:\underline\textsf{Total Investment by Y :}\\\longrightarrow\sf Amount \times Time\\\\\longrightarrow\sf (Rs.\:8000 \times12 \:months)-Rs.(2000\times 6 \:months) \\\\\longrightarrow\sf Rs. \:96000 - Rs. \:12000\\\\\longrightarrow\sf Rs.\:84000$

$\rule{120}{2}$

$\bullet\:\underline\textsf{Total Investment by Z :}\\\longrightarrow\sf Amount \times Time\\\\\longrightarrow\sf Rs.\:6000 \times 6 \:months \\\\\longrightarrow\sf Rs.\:36000$

$\rule{200}{1}$

$\underline{\bigstar\:\textsf{Ratio of Investments :}}$

$\longrightarrow\sf X : Y : Z\\\\\\\longrightarrow\sf Rs.\:60000 : Rs.\:84000 : Rs.\:36000\\\\\qquad\scriptsize{\bf{\dag}\:\texttt{Dividing each term by Rs. 12000}}\\\\\longrightarrow\blue{\sf 5 : 7 : 3}$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{Share of Y :}}$

$:\implies\tt Y = \dfrac{Ratio}{Total\:Ratio}\times Profit \\\\\\:\implies\tt Y = \dfrac{7}{(5 + 7 + 3)} \times 9615\\\\\\:\implies\tt Y = \dfrac{7}{15} \times 9615\\\\\\:\implies\tt Y =7 \times 641\\\\\\:\implies\boxed{\red{\tt Y =Rs.\:4487}}$

⠀

$\underline{\therefore\:\textsf{Share of Y in Profit is \textbf{Rs. 4487}}}$

Answer 2

$\bf{\Huge{\boxed{\tt{\red{ANSWER\::}}}}}$

$\bf{\Large{\underline{\sf{Given\::}}}}$

X and Y started a business with investments of Rs.5000 & Rs.8000 respectively. After 6 month, Y withdrew an amount of Rs.2000 from his investment and Z joined the business with an investment of Rs.6000. If the profit at the end of the year is Rs.9615.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The share of Y.

$\bf{\Large{\underline{\tt{\purple{Explanation\::}}}}}$

We have three Partners include in a business investment:

$\\\bullet\sf{X\:=\:Rs.5000}\\ \\ \bullet\sf{Y\:=\:Rs.8000}\\ \\ \bullet{\sf{Z\:=\:Rs.6000}}$

Therefore,

$\implies\sf{X\:\:\:\:\:\:\:\::\:\:\:\:\:Y\:\:\:\:\:\:\:\::\:\:\:\:\:\:\:Z}$

$\implies\sf{(5000*12)\:\:\:\:\:\::\:\:\:\:\:(8000*6+6000*6)\:\:\:\:\:\:\::\:\:\:\:\:(6000*6)}$

$\implies\sf{(5\cancel{000}*12)\:\:\:\:\:\::\:\:\:\:\:(8\cancel{000}*6+6\cancel{000}*6)\:\:\:\:\:\:\::\:\:\:\:\:(6\cancel{000}*6)}$

$\implies\sf{5*12\:\:\:\:\:\:\::\:\:\:\:\:\:\:8*6+6*6\:\:\:\:\:\:\::\:\:\:\:\:\:\:6*6}$

$\implies\sf{5*\cancel{12}\:\:\:\:\:\:\::\:\:\:\:\:\:\:8*\cancel{6}+6*\cancel{6}\:\:\:\:\:\:\::\:\:\:\:\:\:\:6*\cancel{6}}$

$\implies\sf{5*2\:\:\:\:\:\:\::\:\:\:\:\:8+6\:\:\:\:\:\:\::\:\:\:\:6}$

$\implies\sf{5*\cancel{2}\:\:\:\:\:\:\::\:\:\:\:\:\cancel{8}+\cancel{6}\:\:\:\:\:\:\::\:\:\:\:\cancel{6}}$

$\implies\sf{5\:\:\:\:\:\:\:\::\:\:\:\:\:\:4+3\:\:\:\:\:\:\:\::\:\:\:\:\:\:3}$

$\implies\sf{5\:\:\:\:\:\:\:\::\:\:\:\:\:\:7\:\:\:\:\:\:\:\::\:\:\:\:\:\:3}$

_________________________________

A/q

$\bigstar\:$Let the ratio be R.

$\longmapsto\sf{5R\:+\:7R\:+\:3R\:=\:9615}$

$\longmapsto\sf{15R\:\:=\:\:9615}$

$\longmapsto\sf{R\:=\:\cancel{\dfrac{9615}{15} }}$

$\longmapsto\sf{\red{R\:=\:Rs.641}}$

Now,

$\bf{\Large{\boxed{\sf{\green{Share\:of\:Y=7R\::}}}}}$

$\mapsto\sf{Share\:of\:Y\:=\:7(641)}$

$\mapsto\sf{Share\:of\:Y\:=\:7*641}$

$\mapsto\sf{\red{Share\:of\:Y\:=\:Rs.4487}}$