Question:- X Y and Z can complete a piece of work individually in 6 hours 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work ? {UPSC CSAT 2024]
(a) 6 hours 15 minutes (b) 6 hours 30 minutes
(c) 6 hours 45 minutes (d) 7 hours
Solution:- ‘X‘ can complete a work in individually = 6 hours
‘Y‘ can complete a work in individually = 8 hours
‘Z‘ can complete a work in individually = 8 hours
L. C. M. of 6, 8 and 8 = 24
Let total work = 24 units
One day work of X = 1/6 = 1/6×24 = 4 units
One day work of X = 1/8 = 1/8×24 = 3 units
One day work of X = 1/8 = 1/8×24 = 3 units
Only one person at a time can work in each hour and nobody can work for two consecutive hours.
If we want to complete this work in minimum time so we will have add X maximum times because X works maximum in one hours
X + Y/Z + X + Z/Y + X + Y/Z = 4 + 3 + 4 + 3 + 4 + 3 = 21 units
Remaining works = 24 – 21 = 3 unites
Since, X, works 4 units in one hours
Then, X can work 3units work = 3/4 hours = 3/4 × 60 = 45 minutes
The work will be complet = 6 hours 45 minutes
Answer:- Correct Option (C) 6 hours 45 minutes
Some Other Question
Question 1: – A certain number of men can complete a piece of work in 6k days, where k is natural number. By what percent should the number of men be increased so that the work can be completed in 5k days ? [UPSC CSAT 2024]
Solution:- See full solution