# Time and work questions

## Time And Work

 Question 1
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
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
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
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
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.

There are 5 questions to complete.