ArithmeticA 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 ?

A
1 day
B
2 days
C
5 days
D
3 days

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 $= \frac{1}{10} \times 2 = \frac{1}{5} w o r k$

$Remaining w o r k = 1 - \frac{1}{5} = \frac{4}{5} w o r k$

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 $\frac{15}{4} d a y s$

$\frac{4}{5} t h$ work can complete in $\frac{4}{5} \times \frac{15}{4} = 3 d a y s$

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