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Updated on: 14 Apr 2019, 08:25
Originally posted by DisciplinedPrep on 11 Apr 2019, 23:11.
Last edited by DisciplinedPrep on 14 Apr 2019, 08:25, edited 1 time in total.
Last edited by DisciplinedPrep on 14 Apr 2019, 08:25, edited 1 time in total.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
25% (03:34) correct
75%
(03:04)
wrong
based on 65
sessions
History
Date
Time
Result
Not Attempted Yet
Adam and Bryan can complete a job in 48 hours working together. On an occasion, Adam worked alone for half the time Bryan takes to complete the work, and then Adam left and Bryan came on to work for the period that Adam takes to complete one-third of the work. When Bryan stopped, five-sixths of the work was done. What is the least time that will be taken either by Adam or Bryan to complete the work alone?
A. 96 hours
B. 80 hours
C. 60 hours
D. 72 hours
E. 120 hours
A. 96 hours
B. 80 hours
C. 60 hours
D. 72 hours
E. 120 hours
11 Apr 2019, 23:40
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DisciplinedPrep
Go step wise and you will get the answer..
Let the time be A and B for Adam and Bryan to complete a job alone, so \(\frac{1}{A}+\frac{1}{B}=\frac{1}{48}\)..
Step 1 : Adam worked alone for half the time Bryan takes to complete the work
So, Adam works for B/2 hours and he will complete the work in \(\frac{1}{A}*\frac{B}{2}\)
Step 2 : then Adam left and Bryan came on to work for the period that Adam takes to complete one-third of the work.
So, Bryan works for A/3 hours and he will complete the work in \(\frac{1}{B}*\frac{A}{3}\)
Step 3 : When Bryan stopped, five-sixths of the work was done.
so \(\frac{B}{2A}+\frac{A}{3B}=\frac{5}{6}.....3B^2+2A^2=5AB.....2B^2+2A^2-4AB-AB+B^2=0.......2(B-A)^2+B(B-A)=0....(B-A)+(2B-2A+B)=0....(B-A)+(3B-2A)=0\)
So, two cases..
(I) B=A, then \(\frac{1}{B}+\frac{1}{B}=\frac{1}{48}\)....B=96
(II) 3B=2A or A=3B/2, then \(\frac{2}{3B}+\frac{1}{B}=\frac{1}{48}........\frac{5}{3B}=\frac{1}{48}..... B=\frac{48*5}{3}=16*5=80\)
C
General Discussion
27 Feb 2020, 01:46
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DisciplinedPrep
Solution:
Using efficieny method will make our calculations easier, so let's solve it by using efficiency or rate of doing work
Let \(A\) and \(B\) be the rate of doing work of Adam and Bryan respectively.
- • Total work = t\(ime*rate = 48(A+B)\)
• Work done by Adam in half the time Bryan takes to complete the work = \(\frac{48(A+B)}{B}*\frac{A}{2}\)
• Work done by Bryan in one-third of the time of the Adam to do complete the Work = \(\frac{48(A+B)}{A}*\frac{B}{3}\)
- o \(\frac{5}{6}\) of the Total Work done = \(\frac{48(A+B)}{B}*\frac{A}{2} +\frac{48(A+B)}{A}*\frac{B}{3}\)
o \(\frac{5}{6} * 48(A+B) = \frac{48(A+B)}{B}*\frac{A}{2} +\frac{48(A+B)}{A}*\frac{B}{3}\)
o \(\frac{5}{6} = \frac{A}{2B} + \frac{B}{3A}\)
o \(5AB = 3A^2 + 2B^2\)
o \(3A^2 + 2B^2-5AB = 0\)
o \(3A^2 -3AB +2B^2 -2AB = 0\)
o \(3A(A-B) + 2B(A-B)=0\)
o \((3A-2B)(A-B)=0\)
- Either \(A = B\), or \(3A = 2B\)
- Time taken by Adam or Bryan = \(96\) hours
- Time taken by Bryan = \(\frac{48(A+B)}{B}=\frac{48(2.5A)}{1.5A} =80\).
