SSC CPO 2024 PYQ — Question 147

The correct answer is option 2 i.e. $54{3\over4}$.

Let the total work to be done LCM(64, 48) be 192 units.

Total work = Efficiency × Time

According to the given question,

Efficiency of Rajan = $192 \over 64$ = 3 units/day

Efficiency of Rajat = $192 \over 48$ = 4 units/day

Starting from Rajat, they work on alternate days, 

The work done by Rajat and Rajan in 2 days = 4 + 3 = 7 units

The work done by Rajat and Rajan in (2 × 27) 54 days = 189 units  (7 × 27)

Remaining work = 192 - 189 = 3 units

Now Rajat comes to work, 

Time taken by Rajat to complete 4 units of work = 1 day

Time taken by Rajat to complete 3 units of work = ${1 \over 4} \times 3$ = $3 \over 4$ days

The total time taken by them to complete the work = $54 {3 \over 4}$ days

Hence the work will be completed in $54 {3 \over 4}$ days.