A and B can do a piece of work in 10 days and 6 days respectively. A started the work alone and then after 2 days B joined him till the completion of the work. How long did the work last ?

# A and B can do a piece of work in 10 days and 6 days respectively. A started the work alone and then after 2 days B joined him till the completion of the work. How long did the work last ?

1. A

1 day

2. B

2 days

3. C

5 days

4. D

3 days

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### Solution:

A can do a piece of  work in 1 day $=\frac{1}{10}$

B can do a piece of  work in 1 day $=\frac{1}{6}$

A's 2 days work $=\frac{1}{10}×2=\frac{1}{5}\text{\hspace{0.17em}\hspace{0.17em}}work$

$\text{Remaining\hspace{0.17em}}work=1-\frac{1}{5}=\frac{4}{5}\text{\hspace{0.17em}\hspace{0.17em}}work$

A and B's 1 day work = $\frac{1}{10}+\frac{1}{6}=\frac{3+5}{30}=\frac{8}{30}=\frac{4}{15}$

A & B can complete the total work in

$\frac{4}{5}th$ work can complete in

So the work will complete in 3+2 = 5 days.  +91

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