Question

Asha and Usha stitch 180 shirts in 20 hours, Usha and Nisha can stitch them in 12 hours while Asha and Nisha take 15 hours. How much time (in hours) will be required by
the three together to stitch 180 shirts?
​

Answer 1

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

$\:\:$

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

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• Asha and Usha stitch 180 shirts in 20 hours

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• Usha and Nisha can stitch them in 12 hours

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• Asha and Nisha take 15 hours to stitch them

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

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• Time required by the three together to stitch 180 shirts

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

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• Let asha be "A"

• Let nisha be "N"

• Let usha be "U"

• Let the total time required by the three together to stitch 180 shirts be "x"

$\:\:$

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

$\:\:$

〚 Asha and Usha stitch 180 shirts in 20 hours 〛

$\:\:$

$\underline{\bold{\texttt{1 hour work of A + U :}}}$

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➠ $\sf \dfrac { 1 } { 20 }$ ------ (1)

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〚 Usha and Nisha can stitch them in 12 hours 〛

$\:\:$

$\underline{\bold{\texttt{1 hour work of U + N :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 12 }$ ------- (2)

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〚 Asha and Nisha take 15 hours to stitch them 〛

$\:\:$

$\underline{\bold{\texttt{1 hour work of A + N :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 15 }$ ------- (3)

$\:\:$

$\pink{\bold{Adding \ equation \ (1) + (2) + (3) }}$

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$\sf \longmapsto \dfrac { 1 } { 20 } + \dfrac { 1 } { 12 } + \dfrac { 1 } { 15 } = 1 \ hour \ work \ of \ A + U + U + N + A + N$

$\:\:$

$\sf\longmapsto \dfrac { 3 + 5 + 4 } { 60 } = \ 1 \ hour \ work \ of \ 2A + 2U + 2N$

$\:\:$

$\sf \longmapsto \dfrac { \cancel {12}} { \cancel {60} } = \ 1 \ hour \ work \ of \ 2(A + U + N)$

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$\sf \longmapsto \dfrac { 1} { 5 \times 2} = \ 1 \ hour \ work \ of \ (A + U + N)$

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➜ 1 hour work of (A + U + N) = $\sf \dfrac { 1} { 10}$

$\:\:$

$\underline{\bold{\texttt{"x" hour work of the three together :}}}$

$\:\:$

➠ $\sf \dfrac { 1} { 10} \times x$

$\:\:$

As we assumed that the three together will stitch 180 shirts in "x" hours

$\:\:$

So,

$\:\:$

➜ $\sf \dfrac { 1} { 10} \times x = 1$

$\:\:$

➨ x = 10

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• Hence the three together will take 10 hours to stitch 180 shirts

Answer 2

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

$\:\:$

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

$\:\:$

• Asha and Usha stitch 180 shirts in 20 hours

$\:\:$

• Usha and Nisha can stitch them in 12 hours

$\:\:$

• Asha and Nisha take 15 hours to stitch them

$\:\:$

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

$\:\:$

• Time required by the three together to stitch 180 shirts

$\:\:$

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

$\:\:$

Let asha be "A"

Let nisha be "N"

Let usha be "U"

Let the total time required by the three together to stitch 180 shirts be "x"

$\:\:$

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

$\:\:$

〚 Asha and Usha stitch 180 shirts in 20 hours 〛

$\:\:$

$\underline{\bold{\texttt{1 hour work of A + U :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 20 }$ ------ (1)

$\:\:$

〚 Usha and Nisha can stitch them in 12 hours 〛

$\:\:$

$\underline{\bold{\texttt{1 hour work of U + N :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 12 }$ ------- (2)

$\:\:$

〚 Asha and Nisha take 15 hours to stitch them 〛

$\:\:$

$\underline{\bold{\texttt{1 hour work of A + N :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 15 }$ ------- (3)

$\:\:$

$\pink{\bold{Adding \ equation \ (1) + (2) + (3) }}$

$\:\:$

$\sf \longmapsto \dfrac { 1 } { 20 } + \dfrac { 1 } { 12 } + \dfrac { 1 } { 15 } = 1 \ hour \ work \ of \ A + U + U + N + A + N$

$\:\:$

$\sf\longmapsto \dfrac { 3 + 5 + 4 } { 60 } = \ 1 \ hour \ work \ of \ 2A + 2U + 2N$

$\:\:$

$\sf \longmapsto \dfrac { \cancel {12}} { \cancel {60} } = \ 1 \ hour \ work \ of \ 2(A + U + N)$

$\:\:$

$\sf \longmapsto \dfrac { 1} { 5 \times 2} = \ 1 \ hour \ work \ of \ (A + U + N)$

$\:\:$

➜ 1 hour work of (A + U + N) = $\sf \dfrac { 1} { 10}$

$\:\:$

$\underline{\bold{\texttt{"x" hour work of the three together :}}}$

$\:\:$

➠ $\sf \dfrac { 1} { 10} \times x$

$\:\:$

As we assumed that the three together will stitch 180 shirts in "x" hours

$\:\:$

So,

$\:\:$

➜ $\sf \dfrac { 1} { 10} \times x = 1$

$\:\:$

➨ x = 10

$\:\:$

• Hence the three together will take 10 hours to stitch 180 shirts