Question

1. A can do a piece of work in 12 days, B can do the same work in 8 days, and C can do the same job in th time required by both A and B. If both A and B work together for 3 days, then C completes the job. In how many days C finished the work?

Answer 1

$\sf\small\underline\blue{Given:-}$

$\sf{\longrightarrow A\:can\: work=12\:days}$

$\sf{\longrightarrow B\:can\: work=8\:days}$

$\sf{\longrightarrow C\:can\: work=(A+B)'s\: work}$

$\sf\small\underline\blue{To\:Find:-}$

$\sf{\longrightarrow Work\: finished\:by\:C=?}$

$\sf\small\underline\blue{Solution:-}$

To solve this question at first we have find the work done by A and B in how many days but A and didn't complete the job . Rest Job done by C. As we know that work is assumed by 1 .

$\sf\small\underline{Calculation\: begin:-}$

$\tt{\longrightarrow (A+B)\:can\: work}$

$\tt{\longrightarrow \dfrac{1}{12}+\dfrac{1}{8}}$

$\tt{\longrightarrow \dfrac{2+3}{24}}$

$\tt{\longrightarrow \dfrac{5}{24}}$

• A+B work only 3 day's

$\tt{\longrightarrow (A+B)\:can\: work}$

$\tt{\longrightarrow \dfrac{5}{24}\times\:3}$

$\tt{\longrightarrow \dfrac{5}{8}}$

• Rest work done be C:-

$\sf{\longrightarrow Remaining\:part\:of\:job}$

$\tt{\longrightarrow 1-\dfrac{5}{8}}$

$\tt{\longrightarrow \dfrac{8-5}{8}}$

$\tt{\longrightarrow \dfrac{3}{8}}$

• Now work done by C:-

$\sf{\longrightarrow (A+B)'s\:total\: work=C's\:work}$

$\sf{\longrightarrow work\:done\:by\:C}$

$\tt{\longrightarrow \dfrac{5}{24}\times\dfrac{3}{8}}$

$\tt{\longrightarrow \dfrac{5*3}{24*8}}$

$\tt{\longrightarrow \dfrac{5}{8*8}}$

$\tt{\longrightarrow \dfrac{5}{64}}$

$\sf\large{Hence,}$

$\bf{\longrightarrow work\:done\:by\:C=64\:days}$

Answer 2

Given :-

A can do  a piece of work in 12 days, B can do the same work in 8 days, and C can do the same job in th time required by both A and B. If both A and B work together for 3 days,

To Find :-

In how many days C finished the work?

Solution :-

A can do in 12 days

One day work of A = 1/12

B can do in 8 days

One day work of B = 1/8

C can do in time required by both A and B

A and B can do in 3 days

Now

(1/12 + 1/8) × 3

(2 + 3/24) × 3

5/24 × 3

5/8

Now

The remaining job

(1 - 5/8)

(8 - 5/8)

3/8

Now

Days required for C

5/24 × 3/8

5/8 × 1/8

5/64

Now

Days taken by C = 64