A B C working independently can do a piece of work in 8 16 and 12 days respectively A alone works on...........

Math and Mental Ability Time and work

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 ?

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Complete-Test, Previous year (2023)

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1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Explanation:

Correct option 1: only

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.