Time and work questions

Time And Work

Question 1 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minutes in the tank, how many litres does the tank holds?
A
1200
B
4500
C
7200
D
2400
Question 1 Explanation: 
Leak emptied the tank per minute = 100/10 = 10% of water per hour;

Quantity of water emptied per hour = 4 * 60 = 240;

Thus, 10% = 240 liter;

Hence, capacity of water,

100% = 240*100/10 = 2400 liter.







Question 2 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in
A
9 days
B
10 days
C
6 days
D
5 days
Question 2 Explanation: 
1st Method:

(A+B)'s one day's work = 1/3 part;

(A+B) works 2 days together = 2/3 part;

Remaining work = 1-(2/3) = 1/3 part;

1/3 part of work is completed by A in two days;

Hence, one day's work of A = 1/6;

Then, one day's work of B = 1/3 - 1/6 = 1/6;

So, B alone can complete the whole work in 6 days.

2nd method:

(A+B)'s one day's % work = 100/3 = 33.3%

Work completed in 2 days = 66.6%

Remaining work = 33.4%;

One day's % work of A = 33.4/2 = 16.7%;

One day's work of B = 33.3 - 16.7 = 16.7%;

B alone can complete the work in,

= 100/16.7 = 6 days.

Question 3 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
A
12 days
B
10 days
C
15 days
D
8 days
Question 3 Explanation: 
\begin{align} & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{1}{{15}} + \frac{1}{{10}}} \right) = \frac{1}{6} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}}\,{\text{2}}\,{\text{days}} \cr & = \left( {\frac{1}{6} \times 2} \right) = \frac{1}{3} \cr & {\text{Remaining}}\,{\text{work}} \cr & = \left( {1 - \frac{1}{3}} \right) = \frac{2}{3} \cr & {\text{Now}},\,\frac{1}{{15}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \therefore \frac{2}{3}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{a}}\,{\text{in}} \cr & \left( {15 \times \frac{2}{3}} \right) = 10\,{\text{days}} \cr & {\text{Hence,}}\,{\text{the}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} \cr & = \left( {10 + 2} \right) = 12\,{\text{days}} \cr\end{align}






Question 4 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
A
15
B
18
C
16
D
25
Question 4 Explanation: 
\begin{align} & {\text{Ratio}}\,{\text{of}}\,{\text{times}}\,{\text{taken}}\,{\text{by}}\,{\text{Sakshi}}\,{\text{and}}\,{\text{Tanya}} \cr & = 125:100 \cr & = 5:4 \cr & {\text{Suppose}}\,{\text{Tanya}}\,{\text{Takes}}\,x\,{\text{days}}\,{\text{to}}\,{\text{do}}\,{\text{the}}\,{\text{work}} \cr & 5:4::20:x \cr & \Rightarrow x = \left( {\frac{{4 \times 20}}{5}} \right) \cr & \Rightarrow x = 16\,{\text{days}} \cr & {\text{Hence,}}\,{\text{Tanya}}\,{\text{takes}}\,{\text{16}}\,{\text{days}}\,{\text{to}}\,{\text{complete}}\,{\text{the}}\,{\text{work}} \cr\end{align}
Question 5 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
There was a leakage in the container of the refined oil. If 11 kg oil is leaked out per day then it would have lasted for 50 days, if the leakage was 15 kg per day, then it would have lasted for only 45 days. For how many days would the oil have lasted, if there was no leakage ant it was completely used for eating purpose?
A
120 days
B
72 days
C
100 days
D
80 days
Question 5 Explanation: 
Let x kg of oil be used for the eating purpose, daily, then

(x +11) *50 = (x +15) *45

→ x = 25

Thus, Total quantity of oil,

= (25 +11) *50

= 1800

Hence, required number of days,

= 1800/25 = 72 days.







Question 6 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A
8
B
5 1/2
C
5
D
6
Question 6 Explanation: 
\begin{align} & {\text{B's}}\,{\text{10}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{1}{{15}} \times 10} \right) = \frac{2}{3} \cr & {\text{Remaining}}\,{\text{work}} \cr & = \left( {1 - \frac{2}{3}} \right) = \frac{1}{3} \cr & {\text{Now}},\frac{1}{{18}}{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \therefore \frac{1}{3}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & \left( {18 \times \frac{1}{3}} \right) = 6\,{\text{days}} \cr\end{align}
Question 7 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
If 10 persons can do a job in 20 days, then 20 person with twice the efficiency can do the same job in:
A
5 days
B
10 days
C
40 days
D
20 days
Question 7 Explanation: 
By work equivalence method,

man*days*work = MAN*DAYS*WORK

10*20*1 = 20*2*x

→ x = 5 days.







Question 8 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
A
30 days
B
20 days
C
22 1/2 days
D
25 days
Question 8 Explanation: 
\begin{align} & {\text{Ratio}}\,{\text{of}}\,{\text{times}}\,{\text{taken}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B = 1:3}} \cr & {\text{The}}\,{\text{time}}\,{\text{difference}}\,{\text{is}}\,\left( {{\text{3 - 1}}} \right)\,{\text{2}}\,{\text{days}} \cr & {\text{while}}\,{\text{B}}\,{\text{take}}\,{\text{3}}\,{\text{days}}\,{\text{and}}\,{\text{A}}\,{\text{takes}}\,{\text{1}}\,{\text{day}}{\text{.}} \cr & {\text{If}}\,{\text{difference}}\,{\text{of}}\,{\text{time}}\,{\text{is}}\,{\text{2}}\,{\text{days,}}\,{\text{B}}\,{\text{takes}}\,{\text{3}}\,{\text{days}}{\text{.}} \cr & {\text{If}}\,{\text{difference}}\,{\text{of}}\,{\text{time}}\,{\text{is}}\,{\text{60}}\,{\text{days,}} \cr & {\text{B}}\,{\text{takes}}\,\left( {\frac{3}{2} \times 60} \right) = 90\,{\text{days}} \cr & {\text{So,}}\,{\text{A}}\,{\text{takes}}\,{\text{30}}\,{\text{days}}\,{\text{to}}\,{\text{do}}\,{\text{the}}\,{\text{work}}{\text{.}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{30}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{90}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{1}{{30}} + \frac{1}{{90}}} \right) = \frac{4}{{90}} = \frac{2}{{45}} \cr & \therefore {\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{together}}\,{\text{can}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\, \cr & \frac{{45}}{2} = 22\frac{1}{2}\,{\text{days}}\, \cr\end{align}
Question 9 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A and B working together completed a job in 5 days. If A works twice as efficiently as he actually did and B works 1/3 of actual efficiency, the work would have completed in 3 days. Find the for A to complete the job alone.
A
6 3/4
B
6 1/4
C
6 1/2
D
12 1/2
Question 9 Explanation: 
One Day's work of A and B together,

1/A + 1/B = 1/5. ------ (i)

When A works with twice efficiency,Then,

2/A + 1/3B = 1/3. --------(ii)

on solving equations (i) and (ii), we get

A = 25/4 = 6 1/4.







Question 10 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
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
19
B
13
C
21
D
17
Question 10 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 looses = 26 +7 = Rs. 33.

So, Total idle days = 627/33 = 19 days.

Alternatively,

Let he works for X days and remain idle for (56 - X).

Now, According to question,

X*26 - 7*(56 -X)= 829.

26X + 7X - 392 = 829.

33X = 829 + 392 = 1221.

X = 37 days.

No of days remain idle = 56 -37 - 19 days.

There are 10 questions to complete.

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