Question

6. A and B working together can complete a job in
3 hours, if A alone can do the job in
$7 \times \frac{1}{2}$
hours, in
how much time can B alone finish the job?
​

Answer 1

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Answer 2

Question

6. A and B working together can complete a job in3 hours, if A alone can do the job in $7 \times \frac{1}{2}$ hours.In how much time can B alone finish the job?

Answer

Given:-

•A and B working together can complete a job in 3 hours

• A alone can do the job in $7 \times \frac{1}{2}$ hours

To find:- Time taken by B alone to finish the job.

Solution

We have,

$\tt{(A+B)'s~1hour's~work=\frac{1}{3}}$

$\tt{(A)'s~1hour's~work=\frac{2}{15}}$

$\tt{\therefore~B's~1hour~work=(A+B)'s~1hour's~work-(A)'s~1hour's~work}$

$\tt{(B)'s~1hour's~work=\frac{1}{3}-~\frac{2}{15}}$

$\tt{\mapsto~\frac{1}{3}-~\frac{2}{15}}$

$\tt{\mapsto~\frac{5-2}{15}}$

$\tt{\mapsto~\frac{3}{15}}$

$\tt{\mapsto~\frac{1}{5}}$

$\tt{\mapsto~\frac{1}{B}=\frac{1}{5}}$

${\boxed{\tt{\longmapsto~B=5}}}$

Hence, Time taken by B alone to finish the job is 5 hours.