Question

Pintu is able to be to a piece of work
in 15 days and Sadir can do the same work
in 20 days. If they can work together for
4 days, what is the fraction of work left
ans​

Answer 1

A n s w e r

$\:\:$

G i v e n

$\:\:$

• Pintu is able to complete a piece of work in 15 days

• Sadir can do the same work in 20 days

• They can work together for 4 days

$\:\:$

F i n d

$\:\:$

• Fraction of work left after 4 days of working together

$\:\:$

S o l u t i o n

$\:\:$

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

$\:\:$

Given that , Pintu is able to complete the work in 15 days

$\:\:$

➠ $\sf \dfrac { 1 } { 15 }$

$\:\:$

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

$\:\:$

Given that , Sadir is able to complete the work in 20 days

$\:\:$

➠ $\sf \dfrac { 1 } { 20}$

$\:\:$

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

$\:\:$

➜ $\sf \dfrac { 1 } { 15 } + \dfrac { 1 } { 20 }$

$\:\:$

➜ $\sf \dfrac { 4 + 3 } { 60 }$

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➜ $\sf \dfrac { 7 } { 60 }$

$\:\:$

$\underline{\bold{\texttt{4 days work when they work together :}}}$

$\:\:$

➜ $\sf \dfrac { 7 } { 60 } \times 4$

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➜ $\sf \dfrac { 7 } { 15 }$

$\:\:$

$\underline{\bold{\texttt{Left work after 4 days :}}}$

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➜ $\sf 1 - \dfrac { 7 } { 15 }$

$\:\:$

➜ $\sf \dfrac { 15 - 7 } { 15 }$

$\:\:$

➨ $\sf \dfrac { 8 } { 15 }$

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• Hence the fraction of work left is $\sf \dfrac { 8 } { 15 }$

$\:\:$

Answer 2

Given ::-

• Pitu is able to do a work in 15 days.

• Sadir is able to do a work in 20 days

• They do the same work together for 4 days.

To find ::-

• what is the fraction of work left after working together for 4 days ?

Solution ::-

• Pitu is able to do a work in 15 days.

So, work done by pitu in one day = $\dfrac{1}{15}$

• Sadir is able to do a work in 20 days .

So, work done by Sadir in one day = $\dfrac{1}{20}$.

__________

Work done by both if they work together ::-

$⟼$ $\dfrac{1}{15}$ + $\dfrac{1}{20}$

By , taking L.C.M of 15 and 20

$⟼$ $\dfrac{4+3}{60}$

By , adding 4 + 3

$⟼$ $\dfrac{7}{60}$

_________

work done by both in one day = $\dfrac{7}{60}$

Work done by both in 4 days = $\dfrac{7}{60}$ × 4

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\dfrac{7}{15}$

_________

Remaining work ::-

$⟼$ 1 - $\dfrac{7}{15}$

$⟼$ $\dfrac{15-7}{15}$

$⟼$ $\dfrac{8}{15}$

Hence , Remaining work is $\dfrac{8}{15}$