# 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**.