Neeraj is 4 times as efficient as Dheeraj and together they complete a work in 44 days. How many days will Neeraj alone take to complete the same work?

Let the work be represented by a single job of magnitude $$W$$ (any convenient unit such as “work-units”).

Suppose Dheeraj’s efficiency (work rate) is $$x$$ work-units per day. Given that Neeraj is 4 times as efficient, Neeraj’s efficiency is $$4x$$ work-units per day.

Therefore, when both work together, their combined efficiency is $$x + 4x = 5x$$ work-units per day.

The question says they finish the entire job together in 44 days. Using Work = Rate × Time:

$$W = (5x)\,(44)\;$$ $$\Rightarrow W = 220x$$ $$-(1)$$

Now, to find the number of days Neeraj alone (rate $$4x$$) would need, use again Work = Rate × Time:

Time for Neeraj alone $$= \frac{W}{4x}$$ Substitute $$W$$ from $$(1)$$:

$$\frac{220x}{4x} = 55\text{ days}$$

Hence Neeraj, working by himself, will complete the job in 55 days.

Option C which is: 55 days