Jawaban:

175 days

Penjelasan dengan langkah-langkah:

Let's assume that Q and R worked together for "x" number of days before leaving.

Now, let's find out how much work was completed during the time that all three worked together:

P can complete 1/20 of the job in one day

Q can complete 1/30 of the job in one day

R can complete 1/40 of the job in one day

So, in one day, when all three worked together, they can complete:

1/20 + 1/30 + 1/40 = 2/15

This means that they can complete the whole job in 15/2 days or 7.5 days when they work together.

Now, Q and R worked together for "x" days, which means that they completed (x/30 + x/40) of the job during that time.

The remaining work that P completed alone in 7 days is 1 - (x/30 + x/40) or (8x - 3x)/120 or 5x/120 or x/24.

We know that P completed this remaining work in 7 days, so we can say:

P can complete x/24 of the job in one day

Therefore, P can complete the whole job in 24/x days.

We are given that P completed the remaining work in 7 days, so:

24/x = 1/7

x = 168

Therefore, Q and R worked together for 168/30 + 168/40 = 8.4 + 4.2 = 12.6 days.

So, the total time taken to complete the job is:

168 + 7 = 175 days.