Anirudh and Brahmaji are assigned the work of constructing a wall. Anirudh can do the job in 60 hours alone where as Brahmaji can do the job three times faster. Anirudh starts the work during the first hour and Brahmaji does the work during the second hour. During the third hour both do the job simultaneously. If they continue in this fashion, how long it will take for them to complete the job?

The correct option is 23 hours.

Let us break down the problem step-by-step to calculate the total time required to complete the construction of the wall.

Step 1: Determine individual work rates

Let the total work required to construct the wall be 60 units (since Anirudh takes 60 hours).

Anirudh's work rate per hour:
Anirudh takes 60 hours to complete 60 units of work.
$\text{Anirudh's rate}=\frac{60\text{units}}{60\text{hours}}=1\text{unit/hour}$

Brahmaji's work rate per hour:
Brahmaji works 3 times faster than Anirudh.
$\text{Brahmaji's rate}=3\times 1\text{unit/hour}=3\text{units/hour}$

Step 2: Understand the work pattern

The work is carried out in a 3-hour repeating cycle:

Hour 1: Anirudh works alone and completes 1 unit of work.
Hour 2: Brahmaji works alone and completes 3 units of work.
Hour 3: Both work together and complete (1 + 3) = 4 units of work.

Total work completed in one 3-hour cycle:
$\text{Work per cycle}=1+3+4=8\text{units}$

Step 3: Calculate the work completed in full cycles

Total work to complete = 60 units.
Work done in 1 cycle (3 hours) = 8 units.

Let us find how many full 3-hour cycles fit into 60 units:
$60÷8=7\text{cycles with a remainder of}4\text{units}$

Time taken for 7 full cycles:
$\text{Time}=7\times 3\text{hours}=21\text{hours}$

Work completed after 21 hours (7 cycles):
$\text{Work done}=7\times 8=56\text{units}$

Remaining work = 60 - 56 = 4 units.

Step 4: Calculate time required for the remaining work

Now, we begin the 8th cycle:

22nd Hour (Hour 1 of 8th cycle):
Anirudh works alone and completes 1 unit.
Remaining work = 4 - 1 = 3 units.
Total time so far = 21 + 1 = 22 hours.

23rd Hour (Hour 2 of 8th cycle):
Brahmaji works alone. Brahmaji's rate is 3 units/hour.
Since exactly 3 units of work remain, Brahmaji will complete it in exactly 1 hour.
Remaining work = 3 - 3 = 0 units.
Total time so far = 22 + 1 = 23 hours.

Conclusion:
The wall construction will take a total of 23 hours to complete.