Question

A alone can do a work in 15 days B can do a work in 20 days if they work together for 4 days fraction of work left

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

A alone can do a work in 15 days.

So, it means

$\rm \: \: {A'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{15}$

Further given that,

B alone can do the same work in 20 days.

So, it means

$\rm \: \: {B'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{20}$

Thus, total work done by A and B together in 1 day is

$\rm \: \: {(A + B)'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{15} + \dfrac{1}{20}$

$\rm \: \: {(A + B)'}^{s} \: 1 \: day \: work \: = \: \dfrac{4 + 3}{60}$

$\rm \: \: {(A + B)'}^{s} \: 1 \: day \: work \: = \: \dfrac{7}{60}$

Now, According to statement, they work together for 4 days.

$\rm \: \: {(A + B)'}^{s} \: 4 \: days \: work \: = \: 4 \times \dfrac{7}{60}$

$\rm\implies \: \: {(A + B)'}^{s} \: 4 \: days \: work \: = \: \dfrac{7}{15}$

So, Remaining fraction of work is

$\rm \: = \: 1 - \dfrac{7}{15}$

$\rm \: =  \:\dfrac{15 - 7}{15}$

$\rm \: =  \:\dfrac{8}{15}$

Hence,

$\rm\implies \: \boxed{\rm{  \:Remaining \: fraction \: of \: work = \dfrac{8}{15} \: }}$

Answer 2

Given :-

A can alone can do a work in 15 days B can do a work in 20 days if they work together for 4 days

To Find :-

Work left?

Solution :-

⇒ A could do his total work in 15 days

⇒ Work done by A in one day = 1/15

⇒ B could do his total work in 20 days

⇒ Work done by B in one day = 1/20

Now

⇒ Total work done by A and B in one day = 1/15 + 1/20

⇒ Total work done by A and B in one day = 4 + 3/60

⇒ Total work done by A and B in one day = 7/60

⇒ Total work done by A and B in four days = 4 × 7/60

⇒ Total work done by A and B in four days = 7/15

Now,

⇒ Work left after 4 days = 1 - 7/15

⇒ Work left after 4 days = 15 - 7/15

⇒ Work left after 4 days = 8/15