Short Cuts: Pipes and Cisterns

Short Cuts: Pipes and Cisterns

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Short Cut: 1

If a pipe fills the tank in x hours, and another fills the same tank in y hours and the third fills the tank in z hour. Then the time required, if all the three pipes are open together to fill the tank is:

Example:

Three pipes can fill the tank in 20, 30 and 40 hours respectively. Find the time required to fill the tank if all the pipes are filled simultaneously.

Solution

Here; x= 20, y= 30 and z= 40 hours

Putting the values in

We get answer= 17.14 hours

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Short Cut: 2

If pipe A can fill a tank in x minutes, pipe B can fill the same in y minutes, there is also an outlet C in the Tank. All these are opened simultaneously and the tank takes “T” minutes to get filled. The time in which C can empty the tank in minutes is given by:

Example:

Two pipes can fill a cistern in 60 minutes and 75 minutes respectively. There is also an outlet C, if all the three pipes are opened together, the tanks get filled in 50 minutes. Find the time taken by C to empty the full tank?

Answer:

Here, x= 60, y= 75 and T= 50 minutes, putting the values in equation:

Answer= 100 minutes

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Short Cut 3

A tap M can empty a tank in x minutes, while another tap N can empty it in y minutes. If both the emptying taps are opened together, then the time taken to empty the full tank is:

Example

A tap can empty the tank in 10 minutes; another tap can do the same in 5 minutes. Find the time required by both the taps to empty the tank simultaneously?

Solution

Here x= 10 and y= 5, putting the values we get:

Answer= 3.33 minutes

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 Pipes and Cisterns important facts and formulae

1. Inlet:

A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

2. Outlet:

A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

3. If a pipe can fill a tank in x hours, then:

part filled in 1 hour =1/x

4. If a pipe can empty a tank in y hours, then:

part emptied in 1 hour =1/y

5. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part filled in 1 hour = 1/x−1/y
6. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part emptied in 1 hour = 1/y−1/x

Problems on Ages with Shortcuts

1. The average age of Ram, Venu, Kumar, Gopal and Ragav is 28 years. The average age of Gopal and Ragav is 25 years. What is the average age of Ram, Venu and Kumar ?

Solution :

Here 5 persons' average ( Ram, Venu, Kumar, Gopal and Ragav) age is  = 28 Years.

That means their total age = 5 X 28 = 140 Years.

similarly, average age of two persons (Gopal and Ragav)  is 25 years.

So their total age = 25 X 2 = 50 Years.

here 140 years is the total age of 5 persons             ( Ram, Venu, Kumar, Gopal and Ragav)

50 years is the total age of 2 persons (Gopal and Ragav)

So obviously, the total age of Ram, Venu and Kumar = Total age of  ( Ram, Venu, Kumar, Gopal and Ragav) - Total age of (Gopal and Ragav)

= 140-50 = 90 years.

But here we need average age of these 3 persons.

=> 90/3  = 30 Years

Shortcut Method :

((5 X 28) - (2 X 25)) / 3 =  (140-50)/ 3 = 90/3 = 30 Years

2. The ratio between the ages of Keerthi and Sony is 5:8 respectively and difference between their ages after 5 years will be 12 years. What is the present age of Keerthi ?

Solution :

Usually for these type of questions people start with present age as X and adding 5 to get the ages after 5 years and later solve those equations. But its very time consuming.

A simple logic here is if the age difference between you and your friend is 8 years, after 5 or 10 years also the difference will be same. Hope you are getting what I am trying to say ;)

now see, the ratio between their ages is 5 : 8 

That means their actual ages will be some 5X and 8X

Then the difference between their ages is 5X-8X

in the question it is given that the difference is 12 years =>  5X-8X = 12  => 3X=12  => X = 4

So obviously Keerthi's age = 5(4) = 20

3. Sony is 30 years younger than his mother Rani. Five years ago, Sony was 1/4 as old as his mother was. How old is Sony today ?

Solution :

5 years ago the ratio between their ages was Sony : Jay a= 1X : 4X

we know that Hari is 30 years younger than Rani. That means the difference between their ages is 30.

=>   3X = 30  => X = 10.

But this is the age of 5 years ago. So, the present age will be =10+5 = 15 Years

4. At present the ratio of the ages of Anand and Venkat is 4 : 7 respectively. 6 years hence it will be 7 : 10 respectively. What is the present age of Venkat ?

Solution :

Present ratio of their ages is 4 : 7 (So their present ages will be 4X, 7X)

After six years it will be of 7 : 10

=> (4x+6) : (7x+6) = 7 : 10

=> 40x + 60 = 49X + 42 (Cross Multiplication)

=> 9x = 18

=> x = 2                          

So Venkat's present age will be 7X2 = 14 Years

Shortcut :

There is a shortcut formula for finding X

here, New ratio difference is 3, Added number is 6 (years)

Cross multiplication difference is 49-40 = 9

=>       X = (3 x 6) / 9  = 2

So Venkat's present age will be 7X2 = 14 Years

5. Ten years ago the ratio between the ages of Mohan and Suman was 3:5 respectively. 11 years hence it will be 11:16 respectively. What is the present age of Mohan?

Solution :

 10 years ago 3x : 5x  -------------> Old Ratio

11 years hence  11x : 16x       ------------->  New Ratio

here the difference between ages is 21 years (10 years ago + 11 years hence)

apply above formula here

New ratio difference is (16-11) = 5

Added or substracted number (difference between ages) is = 21

Old and new ratios cross multiplication difference is = 55 - 48 = 7

==> X = (5 x 21) / 7 = 15

present age of mohan is = his age of 10 years ago + 10

                               

                                            = 3x15 + 10 = 55 years

6. Amar is as much younger than Raja as he is older than Kiran. If the ages of Amar and Raja are 30 years and 36 years respectively, what is the age of Kiran now ?

Solution :

Simple logic....

Amar is as much younger than Raja as he is older than Kiran. Try to understand this sentence. According to this sentence you can understand that

·         Amar is younger than Raja that means there is some X years difference between Amar and Raja.

·         Amar is older than Kiranwith same age difference (X years) between Amar and Kiran.

But we know that the ages of Amar and Raja are 30 and 36 years.

So the difference between their ages is = 6 years

So the difference between Amar and Kiran should be = 6 years.

We know the age of Amar as 30 years and Kiran is younger than Amar for 6 years. So he should be of 24 years.

With a single glance you can calculate answer for these type of problems.

7. The average age of a class of 20 students is 20 years. When the age of the teacher is also included, the average will be increased by 2 years. What is the age of the teacher ?

Solution :

Simple logic,

we know that 20 students' average = 20 years

20 people total age = 20 x 20 = 400 years

Including Teacher's

21 people average = 22 years

21 people total age = 21 x 22 = 462

we know the age of 20 students = 400 Yeras

we know the age of 21 people (20 students+ Teacher) = 462

so the age of Teacher will be 462-400 = 62 Years

8. The average age of a wife and husband, who were married 10 years ago, was 20 years then. Including a child the present average age of the family is 23 years. What is the present age of the child?

Solution :

10 year's ago average age = 20 years

10 year's ago total age = 20 x 2 = 40 years.

to calculate their present total age, you should add 20 (10 for wife and 10 for husband) to the age of 10 years ago

=> 40+20 = 60 years (this is the present age of husband and wife)    ----------- (1)

according to the given data, present average age of the family of 3 members is = 23 years

so Total age of 3 members = 23 x 3 = 69 years. ------------------(2)

but we know the present age of Husband and Wife = 60 years

so from equations (1) and (2), we can get the present age of the child is = 9 years

9. Five years ago the average age of a family of five members was 27 years then. Including a child the present average age is still same today. What is the age of the child now ?

Solution :

5 years back average = 27 years

present average should be 5 +27 = 32 Years

So total age of the 5 members at present = 5 x 32 = 160 years  -----------------(1)

but its given that including the child, the present average is 27 years.

=>   the total age of 6 members at present = 6 x 27 = 162 years -----------------(2) 

so from (1) and (2), you can easily get that the present age of the child is 2 years

10. The ratio between the ages of Karan and Arjun is 9:5 and sum of their ages at present is 56 years. How old will karan be after 4 years ?

Solution :

according to given data their ages should be 9x, 5x

their present age = 9x+5x = 56  ==> 14x = 56

so x = 4

so present age of Karan is 9 x 4 = 36 years

after 4 years, 36+4 = 40 years :)