X, Y and Z take 20, 30 and 60 days respectively to complete a job inde

Hello 12921,
I don’t see a way in which Algebra is not used in solving the question. One way or the other, you will have to frame equations in solving this question and that would mean that you are using Algebra to solve this question.

However, by Algebraic method, if you meant the method of assuming work as 1 and obtaining the rates as fractions (THE method we all learned in school to solve questions on Rates) remember that it is not without its share of faults. Therefore, if you think logically, you can use smart values to set up equations and then use Algebra to solve them. Best of both worlds, give it a thought!

The equation to solve Time & Work questions is, Work = Rate * Time

The work can be assumed to be the LCM of 20, 30 and 60, which are the respective times taken by X, Y and Z when working independently.
Let work done = 60 units. To find out the respective rates, we use, Rate = \(\frac{Work }{ Time}\)

Rate of X = \(\frac{60 }{ 20}\) = 3 units per day

Rate of Y = \(\frac{60 }{ 30}\) = 2 units per day

Rate of Z = \(\frac{60 }{ 60}\) = 1 unit per day

At this stage, I have to mention that the question is poorly framed – “They complete a job together”, which is illogical. If that were the case, then we would not have a question at all. It probably means that they started working on the job together.
That sounds more logical.

Y leaves after 4 days. This means that all 3 of them worked together for 4 days.

Rate of X, Y and Z = 3 + 2 + 1 = 6 units per day.
Therefore, work done in 4 days = 24 units.
Remaining work = 36 units.

Z leaves after another 6 days. This means that X and Z work together for 6 days.
Rate of X and Z = 3 + 1 = 4 units per day.
Therefore, work done in 6 days = 24 units.
Remaining work = 36 – 24 = 12 units.

This work has to be completed by X alone. Working at 3 units per day,
Time taken by X to complete 12 units = \(\frac{12 }{ 3}\) = 4 days.

The correct answer is A.