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?
Mohammed
Guys, does anyone know the answer?
get 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? from screen.
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 take12
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 takes12
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?View More RELATED VIDEOS
Algebraic Solution MATHEMATICS Watch in App EXPLORE MORE
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.
Advertisement Remove all ads Sum
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 ?
Advertisement Remove all ads
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 .
Was this answer helpful?
393 32
Guys, does anyone know the answer?