Question 32 (Choice 1) - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

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?

Transcript

Question 32 (Choice 1) 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?Given that
Pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool
Let Time taken by Pipe of larger diameter to fill pool = x hours
∴ Time taken by Pipe of smaller diameter to fill pool = (x + 10) hours
Also, given that
If 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.
Amount of pool filled by larger diameter pipe in 4 hours
+ Amount of pool filled by smaller diameter pipe in 9 hours
𝟒/𝒙+𝟗/(𝒙 + 𝟏𝟎)=𝟏/𝟐
(4(𝑥 + 10) + 9𝑥)/(𝑥(𝑥 + 10))=1/2
(4𝑥 + 40 + 9𝑥)/(𝑥^2 + 10𝑥)=1/2
(13𝑥 + 40)/(𝑥^2 + 10𝑥)=1/2
2(13x + 40) = x2 + 10x
26x + 80 = x2 + 10x
0 = x2 + 10x − 26x − 80
0 = x2 − 16x − 80
x2 − 16x − 80 = 0
Solving by Spitting the middle term
x2 − 20x + 4x − 80 = 0
x(x − 20) + 4(x − 20) = 0
(x + 4) (x − 20) = 0
Splitting the middle term method
We need to find two numbers whose
Sum = −16
Product = 1 × −80 = −80
∴ x = −4, 20
Since x is time, it cannot be negative
∴ x = 20
Now, we need to find
how long it would take for each pipe to fill the pool separately,
Therefore,
Time taken by Pipe of larger diameter to fill pool = x hours
= 20 hours
Time taken by Pipe of smaller diameter to fill pool = (x + 10) hours
= 20 + 10
= 30 hours

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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