Question

'A' can do a piece of a work in 10 days and 'B'can do the same work in
15 days. In how many days can the work be completed if 'A' and 'B'
work together?​

Answer 1

Answer:

Step-by-step explanation:

Given,

'A' can do a piece of work in 10days

'B' can do the same piece of work in 15days

To Find :

In how many days work will complete if  both 'A' and 'B' work together?

Solution:

given,

'A' can do a piece of work in 10days

$\sf\implies$

$1 \:day\: work\: done\: by\: A = \frac{1}{10}$

'B' can do the same piece of work in 15days

$\sf\implies$

$1\: day\: work\: done\: by\: B = \frac{1}{15\\}$

Adding both one day work done by them together:

$\frac{1}{10} + \frac{1}{15}$

L.C.M of 10,15 = 30

$(\frac{1}{10} \times\frac{3}{3} )+(\frac{1}{15}\times\frac{2}{2})$

$= \frac{3}{30} + \frac{2}{30}$

$= \frac{3+2}{30}$

$= \frac{5}{30}$

$= \frac{\not{5}}{\not{30}}$

$= \frac{1}{6}$

hence, if we reciprocaled this this we will get work done by A and B together

$= \frac{1}{\frac{1}{6} }$

= 6

Since, A and B together can complete the work in 6days