Question

A and b together can complete a work in 16 days. A having worked for 8 days, b completes the work in 32 days. In how many days can b alone finish the whole work?

Answer 1

Solution :

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

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.

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

The days shall be B finish the whole work alone.

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

Let A's work in 1 day = r

Let B's work in 1 day = m

We know that total work = 1

A/q

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

&

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

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

Answer 2

Answer:

Step-by-step explanation:

This question is equivalent to saying A & B work together for 16 days completing 16/30 part of work.

Remaining 14/30 part of work is completed by B alone in 44 - 16 = 28 days.

=> B alone can complete work in 28 x 30/14 = 48 days.