Question

A ) a can do a piece of work in 4 days and B can do it in 5 days. How
long will they take if both work together?
B ) A and B working together can do a piece of work in 10 days, B
alone can do the same work in 15 days. How long will A take to
do the same work?​

Answer 1

A)A's 1 day work=1/4

B's 1 day work=1/5

A and B's 1 day work= 1/4+1/5=9/20

They can do the same work in 20/9 days....

Answer 2

A ) A can do a piece of work in 4 days and B can do it in 5 days. How long will they take if both work together?

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$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• A can do a piece of work in 4 days

• B can do it in 5 days

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Days required when they both work together

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

• Let "d" days are required to finish the work when both work together

$\:\:$

$\underline{\bold{\texttt{A's one day work :}}}$

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A can finish the work in 4 days

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➠ $\sf \dfrac { 1 } { 4 }$

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$\underline{\bold{\texttt{B's one day work :}}}$

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B can do it in 5 days

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➠ $\sf \dfrac { 1 } { 5}$

$\:\:$

$\underline{\bold{\texttt{One day work when they both work together :}}}$

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➜ $\sf \dfrac { 1 } { 4 } + \dfrac { 1 } { 5 }$

$\:\:$

➜ $\sf \dfrac { 5 + 4 } { 20 }$

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➜ $\sf \dfrac { 9 } { 20 }$

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$\underline{\bold{\texttt{"d" days work when they both work together :}}}$

$\:\:$

➜ $\sf \dfrac { 9 } { 20 } \times d$

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As we assumed that 'd' days are required to finish the work if they both work together

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So,

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➜ $\sf \dfrac { 9 } { 20 } \times d = 1$

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➨ $\sf d = \dfrac { 20 } { 9 }$

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• Hence working together A & B can finish the work in $\sf \dfrac { 20 } { 9 }$ days

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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\:\:$

B ) A and B working together can do a piece of work in 10 days, B alone can do the same work in 15 days. How long will A take to do the same work?

$\:\:$

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• A and B working together can do a piece of work in 10 days

• B alone can do the same work in 15

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• Days required to finish the work when A works alone

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

• Let A can finish the work alone in "A" days

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { 1 } { A }$

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { 1 } { 15}$

$\:\:$

$\underline{\bold{\texttt{One day work when they work together :}}}$

$\:\:$

➜ $\sf \dfrac { 1 } { A } + \dfrac { 1 } { 15 }$

$\:\:$

$\underline{\bold{\texttt{10 days work when they work together :}}}$

$\:\:$

As given in the question that A & B can finish the work in 10 days

$\:\:$

So,

$\:\:$

➜ $\sf \bigg(\dfrac { 1 } { A } + \dfrac { 1 } { 15 }\bigg) \times 10 = 1$

$\:\:$

➜ $\sf \bigg(\dfrac { 15 + A} { 15A }\bigg) \times 10 = 1$

$\:\:$

➜ 150 + 10A = 15A

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➜ 15A - 10A = 150

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➜ 5A = 150

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➨ A = 30

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• Hence A can finish the work in 30 days