Question

A man purchased sheep for Rs 4500. three sheep were lost and the rest he sold for Rs 30 more per sheep than he paid. if his gain on the whole transaction is 8%. How many sheep did he buy (ans:30)​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{\tt{Given :-}}}$

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• Amount used to by sheep = Rs 4500

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• Number of sheep lost = 3

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• Price at which he selled the sheep is 30 more than that price he used to buy each sheep.

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• He gains 8% profit

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$\red{\underline \bold{\tt{To \: Find :-}}}$

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• Number of sheep he bought

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let the number of sheep he bought was "x"

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$\underline{\bold{\texttt{Cost price of each sheep will be -}}}$

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$\bf \dag \ \ \ Cost price of each sheep = \dfrac { 4500 } { x }$

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$\underline{\bold{\texttt{Selling price of each sheep -}}}$

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$\purple\longrightarrow$ $\sf \dfrac { 4500 } { x } + 30$

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$\underline{\bold{\texttt{Sheep sold -}}}$

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$\purple\longrightarrow$ $\sf x - 3$

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$\underline{\bold{\texttt{Selling price of sheep -}}}$

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$\bf \dag \ \ \ Selling \ price \ of \ sheep \ = \ Number \ of \ sheep \ selled \times selling \ price \ of \ 1 \ sheep$

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$\sf \longmapsto (x - 3) \times (\dfrac { 4500 } { x } + 30)$

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$\underline{\bold{\texttt{Gain percentage -}}}$

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$\bf \dag \ \ \ \dfrac { SP - CP } { CP } \times 100$

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$\sf \longmapsto \dfrac { [(x - 3) \times (\dfrac { 4500 } { x } + 30)] - 4500 } { 4500 } \times 100 = 8$

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$\sf \longmapsto \dfrac { [(x - 3) \times (\dfrac { 4500 + 30x } { x } )] - 4500 } { 4500 } \times 100 = 8$

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$\sf \longmapsto \dfrac {\dfrac { 4500x + 30 x^2 - 13500 - 90x } { x } - 4500 } { 4500 } \times 100 = 8$

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$\sf \longmapsto \dfrac {\dfrac { 30 x^2 - 13500 - 90x } { x } } { 4500 } \times 100 = 8$

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$\sf \longmapsto \dfrac { 30 x^2 - 13500 - 90x } { x } \times \dfrac { 1 } { 4500 } \times 100 = 8$

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$\sf \longmapsto \dfrac { 30 x^2 - 13500 - 90x } { 45x } = 8$

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Dividing numerator and denominator by "15"

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$\sf \longmapsto \dfrac { 2x^2 - 900 - 6x } { 3x } = 8$

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$\sf \longmapsto 2x^2 - 900 - 6x = 24x$

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$\sf \longmapsto 2x^2 - 30x - 900 = 0$

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$\sf \longmapsto x^2 - 15x - 450 = 0$

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$\sf \longmapsto x^2 - 30x + 15x - 450 = 0$

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$\sf \longmapsto x(x - 30) +15(x - 30) = 0$

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$\sf \longmapsto (x - 30)(x + 15) = 0$

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As number of sheep can't be negative so,

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$\bf \dashrightarrow x = 30$

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• Hence total number of sheep he bought was 30