# it can take 12 hours to fill a swimming pool using two pipes. if the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. how long would it take for each pipe to fill the pool separately?

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## It take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smallerdiameterbfor 9 hours only half the pool can be filled .How long would it take for each pipe tobfill the pool separately

It take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smallerdiameterbfor 9 hours only half the pool can be filled .How long would it take for each pipe tobfill the pool separately

Byju's Answer Standard X Mathematics

Elimination Method of Finding Solution of a Pair of Linear Equations

It take 12 ho... Question It take 12

hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for

4

hours and the pipe of smaller diameter for

9

hours only half the pool can be filled .How long would it take for each pipe to fill the pool separately.

Open in App Solution

Let the time taken by the first pipe be

x

hours and the time taken by the second pipe be

y hours.

in 1 hour the first pipe can fill it

= 1 x

in 1 hour the second pipe can fill it

= 1 y 1 x + 1 y = 1 12 --------------(1) 4 x + 9 y = 1 2 ---------------(2) Consider 1 x be a and 1 y be b . a + b = 1 12 -------------(3) 4 a + 9 b = 1 2 ----------------(4)

Multiplying equation (3) by

4 , we get, 4 a + 4 b = 1 3 --------------(5) Now, Equation ( 4 ) − ( 5 ) 5 b = 1 6 b = 1 30 y = 30 .

substituting the value of

y

in equation in (3) we get

Hence the first pipe would takea + 1 30 = 1 12 x = 20 . 20

hours and the second pipe would take

30 **hours.** Suggest Corrections 87

SIMILAR QUESTIONS

**Q.**It can take

12

hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for

9

hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?

**Q.**It takes

12

hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for

9

hours, only half the pool is filled. How long would it take for each pipe to fill the pool separately?

**Q.**it takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool?

**Q.**

Dear sir,

This is the question

Question:

To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool? Please give me the complete step to do this question....

**Q.**Two tubes A and B can fill a swimming pool in 12 and 24 hours respectively. If both the pipes are used together, then how long will it take to fill the tank?

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Elimination Method of Finding Solution of a Pair of Linear Equations

Standard X Mathematics

## It Takes 12 Hours to Fill a Swimming Pool Using Two Pipes. If the Pipe of Larger Diameter is Used for 4 Hours and the Pipe of Smaller Diameter is Used for 9 Hours, Only Half of the Pool is Filled.

It Takes 12 Hours to Fill a Swimming Pool Using Two Pipes. If the Pipe of Larger Diameter is Used for 4 Hours and the Pipe of Smaller Diameter is Used for 9 Hours, Only Half of the Pool is Filled.

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It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool ?

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### SOLUTION

Let the pipe with larger diameter and smaller diameter be pipes A and B respectively.

Also, let pipe A work at a rate of x hours/ unit and pipe B work at a rate of Y hours / unit.

According to the question,

x + y = 112

⇒ 12x + 12y = 1 ....(1)

and 4x + 9y = 12

⇒ 8x + 18y = 1 ...(2)

Multiply (1) by 2 and (2) by 3, We get

24x + 24y = 2 ...(3)

24x + 54y = 3 ....(4)

Subtracting equation (4) from (3),

24x + 24y = 2

- 24x + 54y = 3

- - -

- 30y = - 1 y = 130 Putting y = 130 in equation (1) 12x + 12y = 1 ∴ 12x + 12 x 130 = 1 ∴ 12x + 25 = 1 ∴ 12x = 1 - 25 ∴ x = 35×112 ∴ x = 120

Hence, the pipe with larger diameter will take 20 hours to fill the swimming pool and the pipe with smaller diameter will take 30 hours to fill the swimming pool.

Concept: Simultaneous Linear Equations

Is there an error in this question or solution?

Chapter 6: Simultaneous (Linear) Equations (Including Problems) - Exercise 6 (G) [Page 94]

Q 13 Q 12

### APPEARS IN

Selina Concise Mathematics Class 9 ICSE

Chapter 6 Simultaneous (Linear) Equations (Including Problems)

Exercise 6 (G) | Q 13 | Page 94

## It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?

Click here👆to get an answer to your question ✍️ It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?

Question

## It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?

Medium Open in App

Updated on : 2022-09-05

Let there are two pipes A and B and diameter of A is larger than B.Solution Verified by Toppr Now suppose that

Pipe A take x hours and Pipe B takes y hours to fill the pool separately .

In 1 hour pipe A can fill the pool =

x 1

In 1 hour pipe B can fill the pool=

y 1

If both pipe are together then they take 12 hour to fill the pool.

If the are togther then in 1 hour they fill the pool.

x 1 + y 1 = 12 1 −−−−(1) Now

In 4 hour pipe A can fill the pool is=

x 4

In 9 hour pipe B can fill the pool is=

y 9

than they fill half of the pool,so

x 4 + y 9 = 2 1 −−−−−(2) Now Let x 1 =P & y 1

=Q and puuting in equation 1 &2, than

P+Q= 12 1 ⇒12P+12Q=1−−−−(3) And 4P+9Q = 2 1 ⇒8P+18Q=1−−−−−(4)

Now solving equation 3 & 4

Equation (3) multiplying by 2 and (4) multiplying by 3 and substract.

⇒−30Q=−1 ⇒Q= 30 1

now put value of Q in equation 3

We get P= 20 1 So we found P= 20 1 & Q= 30 1 So x=20 and y=30

Hence the A pipe would take 20 hours and the pipe B would take 30 hours separately .

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