QUESTION

CSAT

Easy

Maths

Prelims 2023

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?

Select an option to attempt

Explanation

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(8, 16, 12) = 48 units

So, Efficiency of A = 48/8=648/8 = 6 units/day

Efficiency of B = 48/16=348/16 = 3 units/day

Efficiency of C = 48/12=448/12 = 4 units/day

The amount of work done in 3 days (Monday + Tuesday + Wednesday) = 6+3+4=136 + 3 + 4 = 13 units Thereafter, the amount of work done in subsequent 3 days (Thursday + Friday + Saturday) = 6+3+4=136 + 3 + 4 = 13 units

Thereafter, the amount of work done in subsequent 3 days (Sunday + Monday + Tuesday) = 6+3+4=136 + 3 + 4 = 13 units

Thereafter, the amount of work done in subsequent 2 days (Wednesday + Thursday) = 6+3=96 + 3 = 9 units

So, amount of work done in 11 days = 13+13+13+9=4813 + 13 + 13 + 9 = 48 units

So, work will get finished in 11 days on Thursday. It means that Statement 1 is correct, but Statement 2 is incorrect.

Hence, option A is correct.

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