Question

A and B together can finish a piece of work in 16 days. A having worked for 8 days, B finishes the remaining work in 32 days. In how many days shall B finish the whole work alone?​

Answer 1

Solution :

$\bf{\large{\underline{\bf{Given\::}}}}$

A and B together can finish a piece of work in 16 days. A having worked for 8 days, B finishes the remaining work alone in 32 days.

$\bf{\large{\underline{\bf{To\:find\::}}}}$

The days shall be B finish the whole work alone.

$\bf{\large{\underline{\bf{Explanation\::}}}}$

Let A's work in 1 day = r

Let B's work in 1 day = m

We know that total work = 1

A/q

$\mapsto\sf{r+m=\dfrac{1}{16}}\\\\\mapsto\sf{r=\dfrac{1}{16} -m............................(1)}$

&

$\mapsto\sf{8r+32m=1}\\\\\mapsto\sf{8\bigg(\dfrac{1}{16}-m\bigg)+32m=1\:\:\:\:[from(1)]}\\\\\mapsto\sf{\dfrac{8}{16} -8m+32m=1}\\\\\mapsto\sf{\dfrac{8}{16} +24m=1}\\\\\mapsto\sf{24m=1-\dfrac{8}{16} }\\\\\mapsto\sf{24m=\dfrac{16-8}{16} }\\\\\mapsto\sf{24m=\dfrac{8}{16} }\\\\\mapsto\sf{m=\cancel{\dfrac{8}{16}} \times \dfrac{1}{24} }\\\\\mapsto\sf{m=\dfrac{1}{2} \times \dfrac{1}{24} }\\\\\mapsto\sf{m=\dfrac{1}{48}}\\\\\mapsto\sf{\red{m=48\:days}}$

Thus;

The B's finish the whole work alone in  = 48 days .

Answer 2

Solution :- (in Simplest way).

Given That, A and B together can finish a piece of work in 16 days.

So,

→ Per day work of (A + B) = (1/16) --------- Equation (1).

Now,

Given That, A worked for 8 days , and B finishes Remaining work in 32 days.

we know That, Total work is 1.

So,

→ 8A + 32B = 1

→ 8A + 8B + 24B = 1

→ 8(A + B) + 24B = 1

Putting value of Equation (1) here , we get,

→ 8 * (1/16) + 24B = 1

→ (1/2) + 24B = 1

→ 24B = 1 - 1/2

→ 24B = 1/2

→ B = 1/(2*24)

→ B = 1/48 . = 48 days.

Hence, B alone can finish The Total work in 48 days.