Question

A, B, C and D can finish a task in 10, 12, 15 and 18 days respectively. They can either choose to work or remain absent on a particular day. If so percent of the total work gets completed after 3 days, then, which of the following options is possible ?

• A. Each of them worked for exactly 2 days.
• B. B and d worked for 1 day each C worked for 2 days and A worked for all 3 days.
• C. A and C worked for 2 days each, D worked for 1 day and B worked for all 3 days.
• D. A and C worked for 1 day each, B worked for 2 days and D worked for all 3 days.

Answer 1

The correct option is D A and C worked for 1 day each, B worked for 2 days and D worked for all 3 days.

Let us assume the amount of work to be finished = LCM of [10,12,15,18] = 180 units.
The amount of work which A can complete in a day $=\frac{180}{10}=18\text{units}$.
The amount of work which B can complete in a day $=\frac{180}{12}=15\text{units}$
The amount of work which C can complete in a day $=\frac{180}{15}=12\text{units}$
The amount of work which D can complete in a day $=\frac{180}{18}=10\text{units}$
It is given that 50 person of the total work gets completed after 3 days. Therefore we can say that 90 units of work was completed in 3 days
Let us check options.
Option (a) : Each of them worked for exactly 2 days.
In this case amount of work completed $=2\times (10+15+12+18)=110\text{units}$.
Option (b) : B and D warked for 1 day each D worked for 1 day and B worked for all 3 days. In this case amount of work completed $=2\times (18+12)+1\times \left(10\right)+3\times \left(15\right)=115\text{units}$.
Option (d): A and C worked for 1 day each B worked for 2 days and D worked for all 3 days.
In this case amount of work completed $=1\times (18+12)+2\times \left(15\right)+3\times \left(10\right)=90\text{units}$.
Therefore we can say that option (d) is the correct answer.