Question

Find two numbers in the ratio of 8:7 such that when each is decreased by 12 1/2 they are in ratio 11:9

Answer 1

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

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

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• Two numbers in the ratio of 8:7

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• When each is decreased by 12 $\rm \dfrac { 1} { 2 }$ they are in ratio 11:9

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

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• The two numbers

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

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Let the numbers be 8x & 7x

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$\underline{\bold{\texttt{Decreased numbers :}}}$

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$\sf \longmapsto 8x - 12 \dfrac { 1 } { 2 }$

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$\: \: \: \: \: \: \: \: \: \: \: \&$

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$\sf \longmapsto 7x - 12 \dfrac { 1 } { 2 }$

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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When each is decreased by 12 $\rm \dfrac { 1} { 2 }$ they are in ratio 11:9

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$\sf \longmapsto \dfrac { 8x - 12 \dfrac { 1 } { 2 } } { 7x - 12 \dfrac { 1 } { 2 } } = \dfrac { 11 } { 9 }$

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$\sf \longmapsto \dfrac { 8x - \dfrac { 25 } { 2 } } { 7x - \dfrac { 25 } { 2 } } = \dfrac { 11 } { 9 }$

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$\sf \longmapsto \dfrac { \dfrac { 16x - 25 } { 2 } } { \dfrac { 14x - 25 } { 2 } } = \dfrac { 11 } { 9 }$

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$\sf \longmapsto \dfrac { 16x - 25 } { 14x - 25 } = \dfrac { 11 } { 9 }$

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$\sf \longmapsto 154x - 275 = 144x - 225$

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$\sf \longmapsto 154x - 144x = 275 - 225$

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$\sf \longmapsto 10x = 50$

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$\sf \longmapsto x = \dfrac { 50 } { 10 }$

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$\bf \dashrightarrow x = 5$

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$\underline{\bold{\texttt{Hence the numbers will be,}}}$

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• 8x = 8(5) = 40

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• 7x = 7(5) = 35

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Hence the numbers are 40 & 35

$\rule{200}5$

Answer 2

Answer:

ur num. is 40and 35 ...........