XAT 2020 — QA & DI Question 11
X, Y, and Z are three software experts, who work on upgrading the software in a number of identical systems. X takes a day off after every 3 days of work, Y takes a day off after every 4 days of work and Z takes a day off after every 5 days of work.
Starting afresh after a common day off,
i) X and Y working together can complete one new upgrade job in 6 days
ii) Z and X working together can complete two new upgrade jobs in 8 days
iii) Y and Z working together can complete three new upgrade jobs in 12 days
If X, Y and Z together start afresh on a new upgrade job (after a common day off), exactly how many days will be required to complete this job?
Answer & solution
- A
2 days
- B
3.5 days
2.5 days
- D
4 days
- E
5 days
Let efficiency per day of X, Y and Z be x, y and z respectively.
Let the amount of work required for an upgrade = T units.
(i) X and Y working together can complete one new upgrade job in 6 days. In 6 days X will work for 5 days and Y will work for 5 days.
∴ 5x + 5y = T …(1)
(ii) Z and X working together can complete two new upgrade jobs in 8 days. X will work for 6 days and Z will work for 7 days.
∴ 6x + 7z = 2T …(2)
(iii) Y and Z working together can complete three new upgrade jobs in 12 days. Y will work for 10 days and Z will work for 10 days.
∴ 10y + 10z = 3T …(3)
Solving (1) , (2) and (3) we get
x = T/10, y = T/10 and z = T/5
If X, Y and Z work together their combined efficiency = T/10 + T/10 + T/5 = 2T/5
∴ Time required by three of them together to complete 1 upgrade = T/(2T/5) = 2.5 days.
Hence, option (c).