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Question

Ishan alone can do a certain piece of work in 'w' days and Bhanumati can do it in '2w' days (w is a positive integer). Both together can do the work in 'x' days (x is another positive integer). Rajat alone can do the work in (w+3) days and Govind can do it in ( 2w-10 ) days. Rajat and Govind together can do it in 'x' days. Mohit alone can do the work in (w-5) days and Mohit and Nirmal together can do the work in 'x' days.

From the information given above which of the following values can be found?

(I) Part of work done by Rajat and Govind together in 8 days.

(II) The number of days taken by Nirmal alone to complete the work.

(III) The most efficient worker among Ishan, Bhanumati, Rajat and Govind.

A Only (I) and (II) Correct Answer Incorrect Answer
B Only (II) and (III) Correct Answer Incorrect Answer
C Only (I) Correct Answer Incorrect Answer
D Only (I) and (III) Correct Answer Incorrect Answer
E All (I), (II) and (III) Correct Answer Incorrect Answer

Solution

ATQ, Given (1/w) + (1/(2w)) = (1/x) ((1/(w + 3)) + ((1/(2w - 10)) = (1/x) [(1/w) + (1/2w)] =  [(1/(w+3)) + (1/(2w-10))] w = 45 Number of days they take to complete the work Ishan : 45 days, Bhanumati : 90 days, Rajat: 48 days and Govind: 80 days; [(1/45) + (1/90)] = (1/x)  x = 30 Let us assume that Nirmal takes 'n' days to complete the work.  [(1/(w - 5)) + (1/n)] = (1/x) = [(1/40) + (1/n)] = (1/30) n = 120; Mohit takes 40 days and Nirmal takes 120 days to complete the work. (I) 8×[(1/48) + (1/80)] is the part of the work completed by Rajat and Govind together in 8 days. (II) Nirmal alone can complete the work in 120 days. (III) In the fractions = (1/45), (1/90), (1/48), (1/80)........ (1/45) is the maximum.  So Ishan is the most efficient.  All three can be answered.

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