Ratnesh and Vinnet worked on alternate days, starting with Ratnesh. The entire work got completed in 54$$\frac{3}{4}$$​ days. If Ratnesh alone can finish the work in 48 days, then in how many days can vinnet alone do the work?

Correct option is B

Given:
Ratnesh and Vinnet worked on alternate days, starting with Ratnesh.
The total time taken to complete the work = $$54\frac{3}{4}$$​ days = $$\frac{219}{4}$$​ days.
Ratnesh alone can finish the work in 48 days.

Formula Used:

Total Work  = Efficiency $$\times$$ Total Time

Solution:

Let efficiency of Ratnesh and Vineet be R and S respectively:

Ratnesh         :       Vineet

27                 :         27

​$$\frac{3}{4}$$                 :

Ramesh work = 27 $$\frac{3}{4}$$ days

Vineet work =  27 days

According to the question,

27$$\frac{3}{4}$$ R + 27 V = 48 R

$$\frac{111}{4}$$ R + 27 V = 48R

​$$\frac{111 R + 108 V }{4}$$ = 48 R

111 R + 108 V = 192 R

108 V = 81 R

​$$\frac{R}{V} = \frac{4}{3}$$  → Efficiency

Total Work = 48 R

Total Work = 48 $$\times$$ 4 = 192 units

Time taken by vineet alone to do work = $$\frac{192}{3}$$ = 64 Days

Thus, the correct option is (b) 64 Days