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Time And Work
Question 11 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
4 days | |
12 days | |
8 days | |
6 days |
Question 11 Explanation:
\begin{align} & {\text{Suppose}}\, {\text{A, }}\, {\text{B}}\, {\text{and}}\, {\text{C}}\, {\text{take}} \cr & x, \, \frac{x}{2}, \, \frac{x}{3}\, {\text{days}}\, {\text{respectively}}\, {\text{to}}\, {\text{finish}}\, {\text{the}}\, {\text{work}} \cr & {\text{Then}}, \, \left( {\frac{1}{x} + \frac{2}{x} + \frac{3}{x}} \right) = \frac{1}{2} \cr & \Rightarrow \frac{6}{x} = \frac{1}{2} \cr & \Rightarrow x = 12 \cr & {\text{So, }}\, {\text{B}}\, {\text{takes}}\, \left( {\frac{{12}}{2}} \right) \cr & = 6\, {\text{days}}\, {\text{to}}\, {\text{finish}}\, {\text{the}}\, {\text{work}} \cr\end{align}
Question 12 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
1/10 | |
8/15 | |
1/4 | |
7/15 |
Question 12 Explanation:
\begin{align} & {\text{A's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{{15}}; \cr & {\text{B's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{{20}}; \cr & \left( {{\text{A + B}}} \right){\text{'s}}\, {\text{1day's}}\, {\text{work}} \cr & = \left( {\frac{1}{{15}} + \frac{1}{{20}}} \right) = \frac{7}{{60}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\, {\text{4}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{7}{{60}} \times 4} \right) = \frac{7}{{15}} \cr & \therefore {\text{Remaining}}\, {\text{work}}\, = \left( {1 - \frac{7}{{15}}} \right) = \frac{8}{{15}} \cr\end{align}
Question 13 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
12 days | |
18 days | |
16 days | |
15 days |
Question 13 Explanation:
\begin{align} & {\text{A's}}\, {\text{2}}\, {\text{day's}}\, {\text{work}} = \left( {\frac{1}{{20}} \times 2} \right) = \frac{1}{{10}} \cr & \left( {{\text{A + B + C}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{60}}} \right) = \frac{6}{{60}} = \frac{1}{{10}} \cr & {\text{Work}}\, {\text{done}}\, {\text{in}}\, {\text{3}}\, {\text{days}} = \left( {\frac{1}{{10}} + \frac{1}{{10}}} \right) = \frac{1}{5} \cr & {\text{Now}}, \, \frac{1}{5}\, {\text{work}}\, {\text{is}}\, {\text{done}}\, {\text{in}}\, {\text{3}}\, {\text{dys}} \cr & \therefore {\text{Whole}}\, {\text{work}}\, {\text{will}}\, {\text{be}}\, {\text{done}}\, {\text{in}}\, \cr & \left( {3 \times 5} \right) = 15\, {\text{days}} \cr\end{align}
Question 14 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
18 days | |
30 days | |
36 days | |
24 days |
Question 14 Explanation:
\begin{align} & {\text{2(A + B + C)'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{1}{{30}} + \frac{1}{{24}} + \frac{1}{{20}}} \right) \cr & = \frac{{15}}{{120}} = \frac{1}{8} \cr & \therefore \left( {{\text{A + B + C}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \frac{1}{{2 \times 8}} = \frac{1}{{16}} \cr & {\text{Work}}\, {\text{done}}\, {\text{by}}\, {\text{A, }}\, {\text{B, }}\, {\text{C}}\, {\text{in}}\, {\text{10}}\, {\text{days}} \cr & = \frac{{10}}{{16}} = \frac{5}{8} \cr & {\text{Remaining}}\, {\text{work}} \cr & = \left( {1 - \frac{5}{8}} \right) = \frac{3}{8} \cr & {\text{A's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{1}{{16}} - \frac{1}{{24}}} \right) = \frac{1}{{48}} \cr & {\text{Now}}, \, \frac{1}{{48}}\, {\text{work}}\, {\text{isdone}}\, {\text{by}}\, {\text{A}}\, {\text{in}}\, {\text{1}}\, {\text{day}} \cr & {\text{So}}, \, \frac{3}{8}\, {\text{work}}\, {\text{will}}\, {\text{be}}\, {\text{done}}\, {\text{by}}\, {\text{A}}\, {\text{in}} \cr & \left( {48 \times \frac{3}{8}} \right) = 18\, {\text{days}} \cr\end{align}
Question 15 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |
If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?
45 | |
60 | |
30 | |
40 |
Question 15 Explanation:
1st method:
A and B complete a work in = 15 days;
One day's work of (A+B) = 1/15;
B complete the work in = 20 days;
One day's work of B = 1/20;
Then, A's one day's work = 1/15 - 1/20 = (4-3)/60 = 1/60;
Thus, A can complete the work in = 60 days.
2nd method: (A+B)'s one day's % work = 100/15 = 6.66%
B's one day's % work = 100/20 = 5%
A's one day's % work = 6.66 - 5 = 1.66%
Thus, A need = 100/1.66 = 60 days to complete the work.
There are 15 questions to complete.