Two boys can do a piece of work in ten days. Three girls can do the same work in five days. In how many days can a boy and a girl together do the work?
(a) 16 days
(b) \(\displaystyle 8\frac{4}{7}\) days
(c) 12 days
(d) \(\displaystyle 5\frac{1}{2}\) days
(e) None of these
Answer for this Time and Work question is (b)
Given that two boys can do the work in ten days, three girls can do it in five days
\(\displaystyle \Rightarrow \) One boy can do the work in 2 \(\displaystyle \times \) 10 = 20 days
One girl can do the work in 3 \(\displaystyle \times \) 5 = 15 days
Therefore, Number of days taken by a boy and a girl working together to finish the work
A works twice as fast as B. If B can complete a work in 24 days independently, the number of days in which A and B can together finish the work is
(a) 12 days
(b) 9 days
(c) 8 days
(d) 6 days
(e) None of these
Answer for this Time and Work question is (c)
Ratio of rates of working of A and B = 2 : 1. So, ratio of times taken = 1 : 2. B’s 1 day’s work = \(\displaystyle \frac{1}{{24}}\) Therefore, A’s one day’s work= \(\displaystyle \frac{1}{{12}}\) (2 times the work of B) (A+B)’s one day’s work= \(\displaystyle \frac{1}{{24}}+\frac{1}{{12}}=\frac{3}{{24}}=\frac{1}{8}\)
So, A and B together can finish the work in 8 days.
Alternate Shortcut:
(The no. Of days are indirectly proportional to the efficiency)
Now Given that,
2x = 24
x = 12 days.
A and B finish the work together = \(\displaystyle \frac{{12\times 24}}{{30}}=8days\)
If one man or three women or five boys can do a piece of work in 46 days will one man, one women and one boy together take to complete the same piece of work?
(a) 30 days
(b) 32 days
(c) 35 days
(d) 40 days
(e) None of these
Answer for this Time and Work question is (a)
If I man(M) or 3 women(W) or 5 boys(B) can do a piece of work in 46 days
The same piece of work will be done by 1 man, 1 woman and 1 boy in
\(\displaystyle \Rightarrow \) Time = total work/(M + W + B)
\(\displaystyle \Rightarrow \) 690/(15 + 5 + 3)
\(\displaystyle \Rightarrow \) 30 days
Therefore, the same piece of work will be done by 1 man, 1 woman and 1 boy in 30 days.
Alternate Method:
1 man +1 woman + 1 boy = \(\displaystyle (5+\frac{5}{3}+1)boys=(\frac{{23}}{3})boys\)
Therefore, required number of days = \(\displaystyle (\frac{{5\times 46\times 3}}{{23}})=30days\)
24 men can complete a piece of work in 15 days. 2 days after the 24 men started working, 4 men left the work. How many more days will the remaining men now take to complete the remaining work?
(a) \(\displaystyle 15\frac{3}{5}\) days
(b) \(\displaystyle 16\frac{4}{5}\) days
(c) \(\displaystyle 11\frac{2}{5}\) days
(d) \(\displaystyle 10\frac{4}{5}\) days
(e) \(\displaystyle 14\frac{1}{5}\) days
Answer for this Objective question of Time and Work is (a)
D = \(\displaystyle \frac{{24\times 13}}{{20}}=\frac{{78}}{5}=15\frac{3}{5}days\)
A, B and C can alone complete a work in 15, 25 and 30 days respectively. A and B started the work and after some days A is replaced by C. Now the work is completed in a further of \(\displaystyle 6\frac{4}{{11}}\) days. How much of the total work did B did?
(a) \(\displaystyle \frac{4}{{11}}\)
(b) \(\displaystyle \frac{4}{{15}}\)
(c) \(\displaystyle \frac{5}{{12}}\)
(d) \(\displaystyle \frac{5}{{11}}\)
(e) \(\displaystyle \frac{2}{{13}}\)
Answer for this Objective question of Time and Work is (d)
Let A replaced by C after x days, so A and B worked for
x days, and then B and C for \(\displaystyle 6\frac{4}{{11}}=\frac{{70}}{{11}}days\) So
So, B worked for \(\displaystyle (5+\frac{{70}}{{11}})=\frac{{125}}{{11}}days\)
In \(\displaystyle \frac{{125}}{{11}}days\), B did \(\displaystyle (\frac{{125}}{{11}})\times (\frac{1}{{25}})=\frac{5}{{11}}ofwork\)
Three pipes P, Q and R can fill a tank in 12, 15 and 20 minutes respectively. If pipe P is opened all the time and pipe Q and R are opened for one hour alternatively. The tank will be full in
(a) 5hr
(b) 6hr
(c) 7hr
(d) 8hr
(e) None of these
Answer for this Objective question of Time and Work is (c)
So in 6 hrs \(\displaystyle \frac{{51}}{{60}}\) is filled. Remaining, \(\displaystyle \frac{9}{{60}}=(\frac{1}{{12}}+\frac{1}{{15}})\times t\)
so T = 1hr
so total = 6 + 1 = 7 hr
A and B undertake to complete a piece of work for Rupees 1200. A can do it in 8 days, B can do it in 12 days and with the help of C they complete the work in 4 days. Find the share of C?
(a) 100
(b) 200
(c) 300
(d) 400
(e) None of these
Answer for this Objective question of Time and Work is (b)
Now efficiency of A, B and C are in the ratio of \(\displaystyle \frac{1}{8}:\frac{1}{{12}}:\frac{1}{{24}}\)
3 : 2 : 1, so share of C is \(\displaystyle \frac{1}{6}\times 1200=200\)
Three pipes A, B, and C can fill the tank in 10 hours, 20 hours and 40 hours respectively. In the beginning all of them are opened simultaneously. After 2 hours, tap C is closed and A and B are kept running. After the 4th hour, tap B is also closed. The remaining work is done by tap A alone. What is the percentage of the work done by tap A alone?
(a) 30 %
(b) 35 %
(c) 45 %
(d) 50 %
(e) None of the Above
Answer for this Objective question of Time and Work is (b)
Pipe A’s work in % = \(\displaystyle \frac{{100}}{{10}}=10\%\)
Pipe B’s work in % = \(\displaystyle \frac{{100}}{{20}}=5\%\)
Pipe C’s work in % = \(\displaystyle \frac{{100}}{{40}}=2.5\%\)
All of them are opened for 2 hours + after 2 hours, tap
C is closed + After the 4th hour, tap B is also closed = 100
