6. There are two inlets and one outlet to a tank. Inlet A and B take 1.5 hours and 2 hours respectively to fill the tank. While outlet C can empty the entire tank in 30 minutes. The gardener decides to open Inlet A at 8 am when he arrives on duty and Inlet B one hour later. Outlet C is opened at 10 am. What will be the time by his watch when the tank will be entirely empty again?
a. 1.25 pm
b. 12 pm
c. 12.12 pm
d. 12.28 pm
Initially tank is empty and after T hours too, it is empty. So, total work done is 0.
This time is needed for tank to get empty.
Exact time will be 4 hours 12 min from 8 am = 12.12 pm
7. Pipes A and B can fill a tank together in 6 hours. When Pipe C is also open, the tank can be filled in 5 hours by 3 pipes together. Pipe A's efficiency is double of Pipe B. How long will Pipe B and C take to fill the tank entirely?
a. 9.75 hours
b. 10. 90 hours
c. 11.25 hours
d. 12.90 hours
But A is twice as fast as B. Hence to do same work, time taken by A is half the time taken by B.
∴ A = ½B
8. Tap A and B can fill a cistern together in 2.4 hours. The water from Tap A flows at the rate of 100 litre per hour to fill the cistern while Tap B has the capacity to fill the entire cistern in just 4 hours. Find how much water can the cistern hold?
a. 500 litres
b. 600 litres
c. 1000 litres
d. 1200 litres
Together they fill the cistern in 2.4 hours
∴ Pipe A can fill 1/6th tank in 1 hour
∴ Pipe a fills the tank completely in 6 hours.
It has a rate of 100 litre water per hour,
So, in 6 hours it gives out 6 x 100 = 600 litres
In 6 hours cistern is full, so capacity = 600 litres
9. A tank has 2 inlets and 1 outlet. The inlets P and Q can fill the tank in 15 hrs and 10 hours respectively. The outlet R take 30 hours to empty the tank. The gardener's son opens all the three pipes by mistake. The gardener realizes this after 2 hours and closes the outlet R so that the tank can be filled. Due to this mistake of his son, how much extra time will be required to fill the tank?
a. 18 minutes
b. 24 minutes
c. 1 hour 20 minutes
d. 2 hours 15 minutes
Normally if Pipe R is closed, then
This is filled by Pipe P and Q only
So total time taken = 2hours + 4.4 hours = 6.4 hours
Extra time taken = 6.4 - 6.0 = 0.4 hours = 24 minutes
10. Three pipes A, B and C when opened simultaneously can fill a tank in 6 hours. C is closed after 2 hours while A and B fill the remaining tank in 7 hours. How long will C take to fill the tank alone?
a. 10 hours
b. 12 hours
c. 13 hours
d. 14 hours
a. 1.25 pm
b. 12 pm
c. 12.12 pm
d. 12.28 pm
Answer: c. 12.12 pm
Explanation:
Let the tank get empty in T hours counting from 8 am.
| A is on for T hours and work done by A = Work in 1 hour x T hours = | T | = | 2T |
| 1.5 | 3 |
| Similarly, B starts at 9 am i.e. it's on for (T-1) hours & work done is = | T-1 |
| 2 |
| Similarly, C starts at 10 am i.e. for (T-2) hours & work done is = | T-2 | = | 2(T-2) |
| 1/2 |
| ∴ | 2T | + | T-1 | - 2(T - 2) = 0 |
| 3 | 2 |
| ∴ T = | 21 | hours = 4.2 hours = 4 hours 12 minutes |
| 5 |
Exact time will be 4 hours 12 min from 8 am = 12.12 pm
7. Pipes A and B can fill a tank together in 6 hours. When Pipe C is also open, the tank can be filled in 5 hours by 3 pipes together. Pipe A's efficiency is double of Pipe B. How long will Pipe B and C take to fill the tank entirely?
a. 9.75 hours
b. 10. 90 hours
c. 11.25 hours
d. 12.90 hours
Answer: c. 11.25 hours
Explanation:
Let Pipe A, B and C fill the tank individually in A, B and C hours respectively.
| Tank filled by Pipe A, B and C together in 1 hour = | 1 | = | 1 | + | 1 | + | 1 |
| 5 | A | B | C |
| Tank filled by Pipe A and B together in 1 hour = | 1 | = | 1 | + | 1 |
| 6 | A | B |
| Tank filled by C in 1 hour = | 1 | - ( | 1 | + | 1 | ) = | 1 | - | 1 | = | 1 |
| 6 | A | B | 6 | 5 | 30 |
∴ A = ½B
| ∴ | 1 | + | 1 | = | 1 |
| ½B | B | 6 |
| ∴ | 1 | = | 1 | hours |
| B | 18 |
| Tank filled by B and C in one hour = | 1 | + | 1 | = | 1 | + | 1 | = | 8 |
| B | C | 18 | 30 | 90 |
| ∴ Tank can be filled in | 90 | = 11.25 hours |
| 8 |
8. Tap A and B can fill a cistern together in 2.4 hours. The water from Tap A flows at the rate of 100 litre per hour to fill the cistern while Tap B has the capacity to fill the entire cistern in just 4 hours. Find how much water can the cistern hold?
a. 500 litres
b. 600 litres
c. 1000 litres
d. 1200 litres
Answer: b. 600 litres
Explanation:
Let Tap A fill the cistern completely in A hours.
| So in 1 hour it fills | 1 | amount of the cistern |
| A |
| Also in 1 hour Tap B fills | 1 | amount of the cistern |
| 4 |
| So, in 1 hour together they'll fill | 1 | amount of the cistern |
| 2.4 |
| Also in 1 hour cistern filled by both is given by | 1 | + | 1 | = | 1 |
| A | 4 | 2.4 |
| ∴ | 1 | = | 1 | - | 1 | = | 1 |
| A | 2.4 | 4 | 6 |
∴ Pipe a fills the tank completely in 6 hours.
It has a rate of 100 litre water per hour,
So, in 6 hours it gives out 6 x 100 = 600 litres
In 6 hours cistern is full, so capacity = 600 litres
9. A tank has 2 inlets and 1 outlet. The inlets P and Q can fill the tank in 15 hrs and 10 hours respectively. The outlet R take 30 hours to empty the tank. The gardener's son opens all the three pipes by mistake. The gardener realizes this after 2 hours and closes the outlet R so that the tank can be filled. Due to this mistake of his son, how much extra time will be required to fill the tank?
a. 18 minutes
b. 24 minutes
c. 1 hour 20 minutes
d. 2 hours 15 minutes
Answer: b. 24 minutes
Explanation:
| In 1 hour, tank filled by Pipe P = | 1 |
| 15 |
| In 1 hour, tank filled by Pipe Q = | 1 |
| 10 |
| In 1 hour, tank emptied by Pipe R = | 1 |
| 30 |
| In one hour tank filled = | 1 | + | 1 | = | 5 |
| 15 | 10 | 30 |
| So entire tank gets filled in | 30 | = 6 hours |
| 5 |
| When Pipe P, Q & R is open, in 1 hour tank filled = | 1 | + | 1 | - | 1 | = | 4 |
| 15 | 10 | 30 | 30 |
| In 2 hours, 2 x | 4 | = | 8 | amount of tank is filled |
| 30 | 30 |
| Remaining tank = 1 - | 8 | = | 22 |
| 30 | 30 |
| In 1 hour, | 5 | amount of tank is filled |
| 30 |
| In ? hours, | 22 | amount of tank is filled |
| 30 |
| ∴ ? hours = | 22/30 | = | 22 | = 4.4 hours |
| 5/30 | 5 |
Extra time taken = 6.4 - 6.0 = 0.4 hours = 24 minutes
10. Three pipes A, B and C when opened simultaneously can fill a tank in 6 hours. C is closed after 2 hours while A and B fill the remaining tank in 7 hours. How long will C take to fill the tank alone?
a. 10 hours
b. 12 hours
c. 13 hours
d. 14 hours
Answer: d. 14
