Question

It takes 8, 12 and 16 days for X, Y and Z respectively to complete a work. How many days will it take to complete the work if X works on it for 2 days, and then Y works on it for until 25% of the work is left for Z to do, and then Z complete the work?

(a) 10 days

(b) 12 days

(c) 8 days

(d) 14 days

Answer 1

Correct option is (b) 12 days

X does the work in 8 days.

∴ In 1 day X does \(\frac 18\)​ work,

Y does the work in 12 days.

∴ In 1 day Y does \(\frac 1{12}\) work and

Z does the work in 16 days.

∴ In 1 day Z does \(\frac 1{16}\)​ work.

So, In 2 days, X does 2 × \(\frac 18\)​ work = \(\frac 14\) ​work,

Now the work left after Y leaves = 25% work = \(\frac 14\)​ work

This is done by Z in \(\frac 14\) × 16 days = 4 days.

So Y's share of work = \(\left(1 - \frac 14 - \frac 14\right)\) work = \(\frac 12\) work

This work he will do in \(\frac 12\) × 12 days = 6 days.

∴ The total number of days required to finish the work

= (2 + 6 + 4) days 

= 12 days.