Question

A and B together can do a piece of work in 15 days. If A's one day work is 1 and half times the one day's work of B, find in how many days can each do the work.


Guys plz solve this
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Answer 1

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

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

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• A and B together can do a piece of work in 15 days

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• A's one day work is $\sf 1 \dfrac { 1 } { 2 }$ the one day's work of B

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

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• Days required for both to do the work alone

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

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• Let A can complete the work in "x" days

• Let B can complete the work in "y" days

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$\underline{\bold{\texttt{One day work of A :}}}$

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➠ $\sf \dfrac { 1 } { x }$

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$\underline{\bold{\texttt{One day work of B :}}}$

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➠ $\sf \dfrac { 1 } { y }$

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

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➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 2 }\times \dfrac { 1 } { y }$

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➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 2y }$ ----- (1)

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$\underline{\bold{\texttt{Their together one day work :}}}$

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➜ $\sf \dfrac { 1 } { x } + \dfrac { 1 } { y }$

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$\underline{\bold{\texttt{15 days work when they work together :}}}$

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➜ $\sf 15(\dfrac{ 1 } { x } + \dfrac { 1 } { y })$ = 1 ---- (2)

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$\underline{\bold{\texttt{Putting \dfrac { 1 } { x } = \dfrac { 3 } { 2y } from (1) to (2) }}}$

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➜ $\sf 15(\dfrac{ 1 } { x } + \dfrac { 1 } { y }) = 1$

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➜ $\sf 15(\dfrac{ 3 } { 2y} + \dfrac { 1 } { y }) = 1$

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➜ $\sf 15(\dfrac{ 3 + 2 } { 2y}) = 1$

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➜ $\sf 15(\dfrac{ 5 } { 2y}) = 1$

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➜ $\sf \dfrac { 75 } { 2y } = 1$

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➜ $\sf 75 = 2y$

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➜ $\sf y = \dfrac { 75 } { 2 }$

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➨ y = 37.5

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• Hence B can complete the work alone in 37.5 days

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$\underline{\bold{\texttt{Putting y = 37.5 in (1) }}}$

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➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 2y }$

$\:\:$

➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 2 \times 37.5}$

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➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 75}$

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➜ $\sf \dfrac { 1 } { x } = \dfrac { 1} { 25}$

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➨ x = 25

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• Hence A can complete the work alone in 25 days

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Therefore A & B alone can complete the work in 25 & 37.5 days

Answer 2

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

$\:\:$

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

$\:\:$

• A and B together can do a piece of work in 15 days

$\:\:$

• A's one day work is $\sf 1 \dfrac { 1 } { 2 }$ the one day's work of B

$\:\:$

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

$\:\:$

• Days required for both to do the work alone

$\:\:$

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

$\:\:$

Let A can complete the work in "x" days

Let B can complete the work in "y" days

$\:\:$

$\underline{\bold{\texttt{One day work of A :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { x }$

$\:\:$

$\underline{\bold{\texttt{One day work of B :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { y }$

$\:\:$

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

$\:\:$

➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 2 }\times \dfrac { 1 } { y }$

$\:\:$

➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 2y }$ ----- (1)

$\:\:$

$\underline{\bold{\texttt{Their together one day work :}}}$

$\:\:$

➜ $\sf \dfrac { 1 } { x } + \dfrac { 1 } { y }$

$\:\:$

$\underline{\bold{\texttt{15 days work when they work together :}}}$

$\:\:$

➜ $\sf 15(\dfrac{ 1 } { x } + \dfrac { 1 } { y })$ = 1 ---- (2)

$\:\:$

$\underline{\bold{\texttt{Putting \dfrac { 1 } { x } = \dfrac { 3 } { 2y } from (1) to (2) }}}$

$\:\:$

➜ $\sf 15(\dfrac{ 1 } { x } + \dfrac { 1 } { y }) = 1$

$\:\:$

➜ $\sf 15(\dfrac{ 3 } { 2y} + \dfrac { 1 } { y }) = 1$

$\:\:$

➜ $\sf 15(\dfrac{ 3 + 2 } { 2y}) = 1$

$\:\:$

➜ $\sf 15(\dfrac{ 5 } { 2y}) = 1$

$\:\:$

➜ $\sf \dfrac { 75 } { 2y } = 1$

$\:\:$

➜ $\sf 75 = 2y$

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➜ $\sf y = \dfrac { 75 } { 2 }$

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➨ y = 37.5

$\:\:$

Hence B can complete the work alone in 37.5 days

$\:\:$

$\underline{\bold{\texttt{Putting y = 37.5 in (1) }}}$

$\:\:$

➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 2y }$

$\:\:$

➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 2 \times 37.5}$

$\:\:$

➜ $\sf \dfrac { 1 } { x } = \dfrac { 3 } { 75}$

$\:\:$

➜ $\sf \dfrac { 1 } { x } = \dfrac { 1} { 25}$

$\:\:$

➨ x = 25

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• Hence A can complete the work alone in 25 days

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• Therefore A & B alone can complete the work in 25 & 37.5 days