## Time and Work Questions and Answers Part-10

1. Three taps A, B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it?
a) 16 minutes
b) 24 minutes
c) 32 minutes
d) 40 minutes

Explanation: A, B and C together can fill 100% empty tank in 10 minutes
Work rate of (A + B + C) = $$\frac{{100}}{{10}}$$ = 10% per minute
A alone can fill the tank in 30 minutes
Work rate of A = $$\frac{{100}}{{30}}$$ = 3.33% per minute
B alone can fill the tank in 40 minutes
Work rate of B = $$\frac{{100}}{{40}}$$ = 2.5%
Work rate of (A + B) = 3.33 + 2.5 = 5.83% per minute
Work rate of C,
= Work rate of (A + B + C) - (A + B)
= 10 - 5.83 = 4.17% per minute
C takes = $$\frac{{100}}{{4.17}}$$ ≈ 24 minutes to fill the tank

2. A and B working separately can do a piece of work in 9 and 15 days respectively. If they work for a day alternately, with A beginning, then the work will be completed in:
a) 9 days
b) 10 days
c) 11 days
d) 12 days

Explanation: Work rate of A = $$\frac{{100}}{9}$$ = 11.11% work per day
Work rate of B = $$\frac{{100}}{{15}}$$ = 6.66% work per day
They together can do (A + B) = 11.11 + 6.66 ≈ 18% work per day
They are working in alternate day, so we take 2 days = 1 unit of day
Therefore, in one unit of day they can complete 18% of work
(A + B) can complete 90% of work in 5 units of days. i.e. (5 × 18)
And the rest 10% work will be completed by A in Next day
Total number of day = 5 Unit of days + 1 day of A
= 2 × 5 + 1 = 11 days

3. Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. Another pipe C can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is also opened. The tank filled up in:
a) 39 min.
b) 46 min
c) 40 min.
d) 45 min.

Explanation: Pipe A can fill empty tank in 36 min.
Pipe A can fill the tank = $$\frac{{100}}{{36}}$$ = 2.77% per minute
Pipe B can fill empty tank in 45 min.
Pipe B can fill the tank = $$\frac{{100}}{{45}}$$ = 2.22% per min.
A and B can together fill the tank
= (2.77 + 2.22) ≈ 5% per minute
So, A and B can fill the tank in 7 min.
= 7 × 5 = 35% of the tank
Rest tank to be filled = 100 - 35 = 65%
C can empty the full tank in 30 min.
C can empty the tank = $$\frac{{100}}{{30}}$$ = 3.33% per min.
C is doing negative work i.e. emptying the tank
A, B and C can together fill the tank,
= 2.77% + 2.22% - 3.33% = 1.67% tank per minute
A, B and C will take time to fill 65% empty tank,
= $$\frac{{65}}{{1.67}}$$ = 39 min. (Approx)

4. Three men A, B, C working together can do a job in 6 hours less time than A alone, in one hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the job in:
a) $$\frac{2}{3}$$ hours
b) $$\frac{3}{4}$$ hours
c) $$\frac{3}{2}$$ hours
d) $$\frac{4}{3}$$ hours

Explanation: Time taken by A =x hours.
Therefore taken by A, B and C together = (x - 6)
Time taken by B = (x - 5)
Time taken by C = 2(x - 6)
Now, rate of work of A + Rate of work of B + Rate of work of C = Rate of work of ABC.
$$\frac{1}{x} + \frac{1}{{x - 5}} + \frac{1}{{2\left( {x - 6} \right)}} = \frac{1}{{x - 6}}$$
On solving above equation, x = 3, $$\frac{{40}}{6}$$
When x = 3, the expression (x - 6) becomes negative, thus it's not possible.
$$x = \frac{{40}}{6}$$
Time taken by A & B together = $$\frac{1}{{\frac{3}{{20}} + \frac{3}{5}}}$$
= $$\frac{4}{3}$$ hours

5. A does half as much work as B in one -sixth of the time.If together they take 10 days to complete a work, how much time shall B take to do it alone?
a) 13.33 days
b) 20 days
c) 30 days
d) 40 days

Explanation: Given,
$${\text{A}} \times \frac{1}{6} = {\text{B}} \times \frac{1}{2}$$
A = 3B
Given they together complete the work in 10 days
So, One Day's work of,
(A + B) = $$\frac{{100}}{{10}}$$ = 10%
(3B + B) = 10%
4B = 10%
one day work of B = $$\frac{{10}}{4}$$ = 2.5%
B can complete 100% work in = $$\frac{100}{2.5}$$ = 40 days

6. An employee pays Rs. 26 for each day a worker and forfeits Rs. 7 for each day he idle. At the end of 56 days, if the worker got Rs. 829, for how many days did the worker remain idle?
a) 21 days
b) 15 days
c) 19 days
d) 13 days

Explanation: His Per day pay = Rs. 26
Total pay employee got = Rs. 829
Total pay he gets if he did not remain idle a single day,
= 26 × 56 = Rs. 1456
He Forfeits or fined = 1456 - 829 = Rs. 627
Per day he Forfeits Rs. 7 Means per idle day he loses = 26 + 7 = Rs. 33
Total idle days = $$\frac{{627}}{{33}}$$ = 19 days

7. A is 60% more efficient than B. In how many days will A and B working together complete a piece of work which A alone takes 15 days to finish?
a) $$\frac{{124}}{{13}}$$ days
b) $$\frac{{113}}{{13}}$$ days
c) $$\frac{{108}}{{13}}$$ days
d) $$\frac{{120}}{{13}}$$ days

Explanation: Given,
A is 60% more efficient of B Means,
\eqalign{ & {\text{A}} = {\text{B}} + 60\% \,{\text{of B}} \cr & {\text{A}} = {\text{B}} + \frac{{60{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{100{\text{B}} + 60{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{160{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{8{\text{B}}}}{5} \cr}
A can complete whole work in 15 days. So,
One day work of A = $$\frac{1}{{15}}$$
One day work of A = $$\frac{{8{\text{B}}}}{5}$$ = $$\frac{1}{{15}}$$
One day work of B = $$\frac{5}{{120}}$$ = $$\frac{1}{{24}}$$
One day work, (A + B) = $$\frac{1}{{15}} + \frac{1}{{24}}$$
One day work, (A + B) = $$\frac{{24 + 15}}{{360}}$$   = $$\frac{{39}}{{360}}$$
Time taken to finish the work by A and B together = $$\frac{{360}}{{39}}$$ = $$\frac{{120}}{{13}}$$ days

8. A pipe can fill a tank in 0.9 hours and another pipe can empty in 0.7 hours. If tank is completely filled and both pipes are opened simultaneously then 450 liters of water is removed from the tank is 2.5 hours. What is the capacity of the tank?
a) 200 liters
b) 350 liters
c) 456 liters
d) 567 liters

Explanation: Pipe A can fill the empty tank in = 0.9 hours
So work rate of the Pipe A = $$\frac{{100}}{{0.9}}$$ % per hour
Pipe B can empty the tank in = 0.7 hours
Negative Work rate of B = $$\frac{{100}}{{0.7}}$$ % per hour. (B is removing water, so, taken as negative work)
Tank fill per hour = $$\frac{{100}}{{0.7}} - \frac{{100}}{{0.9}}$$   = 31.75% per hour
Time Taken to empty the tank = $$\frac{{100}}{{31.75}}$$  ≈ 3.15 hours
Capacity of the tank = 3.15 × 180 = 567 liters

9. 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 :
a) $$\frac{1}{4}$$
b) $$\frac{1}{{10}}$$
c) $$\frac{7}{{15}}$$
d) $$\frac{8}{{15}}$$

\eqalign{ & {\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 & = {\frac{1}{{15}} + \frac{1}{{20}}} = \frac{7}{{60}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{4}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{7}{{60}} \times 4} = \frac{7}{{15}} \cr & {\text{Remaining}}\,{\text{work}}\, = {1 - \frac{7}{{15}}} = \frac{8}{{15}} \cr}
a) $$9\frac{1}{5}$$ days
b) $$9\frac{2}{7}$$ days
c) $$9\frac{3}{5}$$ days
\eqalign{ & \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{4} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{16}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{12}} \cr & {\text{C's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{4} - \left( {\frac{1}{{16}} + \frac{1}{{12}}} \right) = {\frac{1}{4} - \frac{7}{{48}}} = \frac{5}{{48}} \cr & {\text{C}}\,\,{\text{alone}}\,{\text{can}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}} \cr & \frac{{48}}{5} = 9\frac{3}{5}\,{\text{days}} \cr}