Question

years
A does a work in 10 days and B does the same
work in 15 days. In how many days they together
will do the same work ?
​

Answer 1

Explanation:

Method 1:

Firstly, you can assume a number and assign it to the amount of work needed to be completed. The best way to assume the number is to take the LCM of no. Of days which both A and B are taking.

Here, you can take the LCM of 15 and 10. Which is 30.Now, this 30 is the amount of work which is required to be completed.

Now, if A is completing it in 10 days, which means, he is doing 3 units of work everyday.

Similarly, B is doing 2 units of work everyday to complete it in 15 days.

So, if they will work together, they will complete 3+2=5 units of work everyday.

Now, assume they complete the work in x days.

So, x*5=30->x=6

Therefore, the answer is 6 days.Method 2-

Since A is completing the work in 10 days, so in one day, he would be doing 1/10th of the total work.

Similarly, B would be doing 1/15th of the total work in 1 day.

Now if both of them unite, they will do (1/15+1/10)the of the total work in one day.

Which is 5/30 or 1/6

So, in one day, they are doing 1/6th of the total work.

Hence, to complete the work, they required 6 days.

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Answer 2

Let 1 man 1 day work = x

1 boy 1 day work = y

then 5x + 2y = 4(x+y)

=> x = 2y

=> x/y = 2/1

=> x:y = 2:1

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