Question

Radha can do a piece of wok in 25 days and Rekha can do the same work in 20 days. They work together for
5 dyas and then Radha leaves. In how many days will Rekha finish the remaining wo​

Answer 1

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

• Radha can do a piece of work in 25 days
• Rekha can do a piece of work in 20 days
• They both worked together for 5days

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• If radha and rekha worked together for 5 days , in how many days rekha will complete the remaining work ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

Radha's one day work = $\sf {\bold{ \dfrac{1}{25}}}$

⠀⠀⠀⠀

Rekha's one day work = $\sf{\bold{ \dfrac{1}{20}}}$

⠀⠀⠀⠀

( Rekha + Radha )'s one day work = $\sf {\bold{ \dfrac{1}{25} + \dfrac{1}{20}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf {\bold{ \dfrac{1\times 4 + 1\times 5}{100}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf {\bold{ \dfrac{4+5}{100}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf {\bold{ \dfrac{9}{100}}}$

⠀⠀⠀⠀

( Rekha + Radha)'s 5 days work = $\sf {\bold{ \dfrac{9\times 5}{100}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf {\bold{ \dfrac{9}{20}}}$

⠀⠀⠀⠀

• let total work be 1

⠀⠀⠀⠀

Work left = Total work - work done

⠀⠀⠀⠀

Work left = $\sf {\bold{ 1 - \dfrac{9}{20}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀= $\sf {\bold{ \dfrac{20 - 9}{20}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀= $\sf {\bold{ \dfrac{11}{20}}}$

⠀⠀⠀⠀

No. of days Rekha will take to complete the remaining work = $\sf {\bold{ \dfrac{Work\: left }{Rekha's\: one\: day \: work}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf {\bold{ \dfrac{\dfrac{11}{20}}{\dfrac{1}{20}}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf {\bold{ \dfrac{11 \times 20 }{20\times 1}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 11 days

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Rekha will take 11 days to complete the remaining work

Answer 2

Step-by-step explanation:

Radha's one day work = \sf {\bold{ \dfrac{1}{25}}}

25

1

⠀⠀⠀⠀

Rekha's one day work = \sf{\bold{ \dfrac{1}{20}}}

20

1

⠀⠀⠀⠀

( Rekha + Radha )'s one day work = \sf {\bold{ \dfrac{1}{25} + \dfrac{1}{20}}}

25

1

+

20

1

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= \sf {\bold{ \dfrac{1\times 4 + 1\times 5}{100}}}

100

1×4+1×5

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= \sf {\bold{ \dfrac{4+5}{100}}}

100

4+5

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= \sf {\bold{ \dfrac{9}{100}}}

100

9

⠀⠀⠀⠀

( Rekha + Radha)'s 5 days work = \sf {\bold{ \dfrac{9\times 5}{100}}}

100

9×5

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= \sf {\bold{ \dfrac{9}{20}}}

20

9

⠀⠀⠀⠀

let total work be 1

⠀⠀⠀⠀

Work left = Total work - work done

⠀⠀⠀⠀

Work left = \sf {\bold{ 1 - \dfrac{9}{20}}}1−

20

9

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀= \sf {\bold{ \dfrac{20 - 9}{20}}}

20

20−9

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀= \sf {\bold{ \dfrac{11}{20}}}

20

11

⠀⠀⠀⠀

No. of days Rekha will take to complete the remaining work = \sf {\bold{ \dfrac{Work\: left }{Rekha's\: one\: day \: work}}}

Rekha

′

sonedaywork

Workleft

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= \sf {\bold{ \dfrac{\dfrac{11}{20}}{\dfrac{1}{20}}}}

20

1

20

11

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= \sf {\bold{ \dfrac{11 \times 20 }{20\times 1}}}

20×1

11×20

⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 11 days