Quantitative Aptitude
TIME AND WORK MCQs
Time & Work, Work And Wages
- Two workers A and B are engaged to do a piece of work. A, working alone, would take 8 hours more to complete the work than if both of them work together. If B worked alone he would take 4 hours more to complete the work than they both need working together. The time required for both of them to finish the work together is
A's 1 day's work = \(\frac{1}{15};\)
B's 1 day's work = \(\frac{1}{20};\)
(A + B)'s 1 day's work = \(\left(\frac{1}{15}+\frac{1}{20}\right)= \frac{7}{60}.\)
(A + B)'s 4 day's work = \(\left(\frac{7}{60}\times4\right)= \frac{7}{15}.\)
Therefore, Remaining work = \(\left(1-\frac{7}{60}\right)= \frac{8}{15}.\)
\(9\frac{1}{5}days\)(A + B + C)'s 1 day's work = \(\frac{1}{4}, \)
A's 1 day's work = \(\frac{1}{16},\)
B's 1 day's work = \(\frac{1}{12}.\)
So, C's 1 day's work = \(\frac{1}{4}-\left(\frac{1}{16}+\frac{1}{12}\right)= \left(\frac{1}{4}-\frac{7}{48}\right)=\frac{5}{48}\)
So, C alone can do the work in \(\frac{48}{5}=9\frac{3}{5}days\)
A's 2 day's work = \(\left(\frac{1}{20}\times2\right)=\frac{1}{10}.\)
(A + B + C)'s 1 day's work = \(\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{60}\right)=\frac{6}{60}=\frac{1}{10}.\)
Work done in 3 days = \(\left(\frac{1}{10}+\frac{1}{10}\right)=\frac{1}{5}\)
Now, \(\frac{1}{5}\) work is done in 3 days.
So, Whole work will be done in (3 x 5) = 15 days.
Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes \(\left(\frac{3}{2}\times60\right)\) = 90 days.
So, A takes 30 days to do the work.
A's 1 day's work = \(\frac{1}{30}\)
B's 1 day's work = \(\frac{1}{90}\)
(A + B)'s 1 day's work = \(\left(\frac{1}{30}+\frac{1}{90}\right)=\frac{4}{90}=\frac{2}{45}.\)
A and B together can do the work in \(\frac{45}{2}=22\frac{1}{2}days\)
C's 1 day's work = \(\frac{1}{3}-\left(\frac{1}{6}+\frac{1}{8}\right)=\frac{1}{3}-\frac{7}{24}=\frac{1}{24}.\)
A's wages : B's wages : C's wages = \(\frac{1}{6}:\frac{1}{8}:\frac{1}{24}=4:3:1.\)
So, C's share (for 3 days) = Rs. \(\left(3\times\frac{1}{24}\times3200\right)\) = Rs. 400.