Q. A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on.
Consider the following statements:
1. The work will be finished on Thursday.
2. The work will be finished in 10 days.
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Correct Answer: (a) 1 only
Question from UPSC Prelims 2023 CSAT
Explanation :
A, B, C work independently on alternate days
A, B, C working independently can do a piece of work in 8, 16, and 12 days respectively.
Let the total amount of work be LCM (8, 16, 12) = 48 units
So, Efficiency of A = 48/8 = 6 units/day
Efficiency of B = 48/16 = 3 units/day
Efficiency of C = 48/12 = 4 units/day
The amount of work done in 3 days (Monday + Tuesday + Wednesday) = 6 + 3 + 4 = 13 units
The cycle of work then repeats every 3 days.
To find out when the work will be finished, we need to find out how many full cycles of 3 days can be completed before the total work of 48 units is done.
48 units / 13 units per cycle = 3 cycles with a remainder of 9 units
This means that 3 full cycles of 3 days will be completed, which is 9 days, and 9 units of work will be remaining.
On the 10th day (Monday), A will work and do 6 units. This leaves 3 units of work remaining.
On the 11th day (Tuesday), B will work and do 3 units, completing the work.
So, the work will be finished on the 11th day, which is a Thursday.
Therefore, statement 1 is correct and statement 2 is incorrect.
Hence, the correct answer is option (a) 1 only.
