Question

4. Aisha and Palak can do a piece of work in 25 and 20 days respectively. They began the work together but Palak left after some days and Aisha completed the rest of the work in 16 days. After how many days did Palak leave?

Answer 1

Time taken by Aisha alone to complete the work = 25 days
So, in 1 day she will do = 1/25 work

Time taken by Palak alone to complete the work = 20 days
So, in 1 day she will do = 1/20 work
Together they will do in 1 day = 1/25 + 1/20 work
= 4/100 + 5/100 work = 9/100 work

Now,
After Palak left after some days, time taken by Aisha to complete the work = 16 days
Work she did in 16 days = 16 * 1/25 = 16/25
So, Work done by both of them before Palak left = 1 - 16/25 = 9/25
9/25 work is done by both together
Together they will do in 1 day = 9/100 work
Together they will do work in  = 100/9 days

Together they will do 9/25 work in = 100/9 * 9/25 days
= 4 days
Therefore, Palak left after 4 days

Answer 2

Given conditions ⇒

Aisha can do a piece of work in 25 Days.
∴ Aisha's one day work = 1/25 

Palak can do a piece of work in 20 Days.
∴ Palak's 1 day work = 1/20

Now, Total work done by Aisha and Palak in 1 day = 1 day work of Aisha + 1 Day work of Palak.
 = 1/25 + 1/20
 = (4 + 5)/100
 = 9/100

∴ Total time taken by the Aisha and Palak to complete the [Pice of the Work = 100/9 Days.

Now, Aisha and Palak  completed the Piece of work together in 1 day = 1 -  Work done by the Aisha in last 16 Days.

∵ Work done by the Aisha in 16 Days = 16 × Aisha's one day work
 = 16 × 1/25
 = 16/25

∴ Work done by Aisha and Palak before the Palak's left = 1 - 16/25
= (25 - 16)/25
= 9/25 

Now, 
 9/25 work is done by the Aisha and the Palak together in  100/9 Days.
∴ Total work done by Aisha and Palak together = 100/9 × 9/25
  = 4 Days.

Days after which the Palak leave will be equal to the Time taken by Palak and Aisha together to complete the work. 

Hence, the Palak left after the 4 days.


Hope it helps.