Question

Amit finished a piece of work in 8 days and sumit finished the same work in 10 days . How much time will they take to finish the work if both work togather

Answer 1

Answer:

4.44 days

Step-by-step explanation:

Amit finished a piece of work in 8 days

Amit's 1 day work = $\frac{1}{8}$

Sumit finished Same piece of work in 10 days

Sumit's 1 day work = $\frac{1}{10}$

Amit + Sumit's 1 day work =  $\frac{1}{8} + \frac{1}{10}$

= $\frac{1}{40} \times (5 + 4)$

= $\frac{1}{40} \times (9)$

= $\frac{9}{40}$

Time taken to finish work By Amit & Sumit together = $\frac{1}{\frac{9}{40}}$

= $\frac{40}{9}$

=  4.44 days

Answer 2

Amit can finish work in=8 days
Amit 1 day Work=$\frac{1}{8}$

Sumit Can finish work in=10 days
Sumit 1 day work=$\frac{1}{10}$

If They Work Together
=$\frac{1}{8}$+$\frac{1}{10}$
=$\frac{5+4}{40}$ LCM=40
=$\frac{9}{40}$

(Amit +Sumit ) 1 day work=$\frac{9}{40}$
Amit+Sumit Can complete Work in=$\frac{40}{9} \:days$

$\boxed{\mathbf{Days=4 \frac{4}{9} }}$