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Ratnesh and Vinnet worked on alternate days, starting with Ratnesh. The entire work got completed in 5434\frac{3}{4}43​​ days. If Ratnesh alone can fi
Question

Ratnesh and Vinnet worked on alternate days, starting with Ratnesh. The entire work got completed in 5434\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?

A.

60

B.

64

C.

66

D.

62

Correct option is B

Given:
Ratnesh and Vinnet worked on alternate days, starting with Ratnesh.
The total time taken to complete the work = 543454\frac{3}{4}​ days = 2194\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

34\frac{3}{4}                 :

Ramesh work = 27 34\frac{3}{4} days

Vineet work =  27 days

According to the question,

2734\frac{3}{4} R + 27 V = 48 R

1114\frac{111}{4} R + 27 V = 48R

111R+108V4\frac{111 R + 108 V }{4} = 48 R

111 R + 108 V = 192 R

108 V = 81 R

RV=43\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 = 1923\frac{192}{3} = 64 Days

Thus, the correct option is (b) 64 Days 

Exam Hall Method: 

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