Question

A and B working separately can do a piece of work in 9 nd 15 days respectively if they work for a day alternately. with A beginning. then the work will be completed in how many days

Answer 1

here is the answer.................

Answer 2

Given:

A alone can do a piece of work in 9 days

B alone can do a piece of work in 15 days

A and B work on alternate days

To find:

The required no. of days in which the work will be completed

Solution:

We have,

In 1 day, the amount of work done by A will be $\frac{1}{9}$

In 1 day, the amount of work done by B will be $\frac{1}{15}$

As given in the question that A and B will be working separately on the alternate days starting with A, so let us first understand the pattern of their work i.e.,

A    B    A     B    A    B ……..

From the above pattern, we can see that  

• The amount of work done in 1st & 2nd day will be first done by A and then by B i.e., ($\frac{1}{9} + \frac{1}{15}$) of the total work

• The same amount of work will be done on the 3rd & 4th day, then on the 5th & 6th days and so on.  

• From this, we get that the cycle will be repeated every 2 days.

∴ The amount of work done in the first 2 days, $= \frac{1}{A} + \frac{1}{B} = \frac{1}{9} + \frac{1}{15} = \frac{5+3}{45} = \frac{8}{45} \:of\:the\:total\:work$  

Since nothing is specified in the question so we will consider the total work to be done is 1 unit of work.

Now, we will convert 8/45 unit of work into 1 unit of work

2 days → 8/45 units

8 is not a direct multiple of 45 so we will multiply 8 in such a way that it is as close as 45 i.e.,

we will multiply with 5 on both the sides

5 * (2 days) → 5 * (8/45 units)

10 days → 40/45 units of work are completed in 10 days  

Since B has been working on every even no. of days, therefore, B has worked on the 10th day.

∴ The remaining amount of work to be done by A on the 11th day will be,

= 1 – $\frac{40}{45}$

= $\frac{45 - 40}{45}$

= $\frac{5}{45}$

= $\frac{1}{9}$ units of the total work  

We know that A does 1/9 units of work in 1 day

∴ The required time to complete the whole work = 10 + 1 = 11 days

Thus, the work will be completed in 11 days.

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