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It can 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?

Solution:

Let us consider the time taken by the pipe of larger diameter to fill the pool to be x hours.

Let us consider the time taken by the pipe of smaller diameter alone to y hours.

In 1 hour the pipe of larger diameter fills 1/ x part of the pool.

In 4 hours, the pipe of larger diameter fills 4/ x parts of the pool.

In 9 hours, the pipe of smaller diameter fills 9/ y parts of the pool.

As per the question,

4/x + 9/y = 1/2---------------------------(1)

Using both the pipes, the pool is filled in 12 hours,

12/x + 12/y = 1---------------------------(2)

Consider

1/ x = u

1/y = v .

On rearranging, we get,

4u + 9v = 1/2------------------------(3)

12u + 12v = 1------------------------(4)

Solve the linear equations (3) and (4)

Multiplying (3) by 3 and subtracting (4),we get,

15v = 1/2

v = 1/30.

Substituting the value of v in (4),we get,

u = 1/20

v = 1/30.

1/x = 1/20.

1/y = 1/30.

x = 20

y = 30.

Therefore, the pipe of larger diameter alone can fill the pool in 20 hours and the pipe of smaller diameter alone can fill the pool in 30 hours.

✦ Try This: It can take 10 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 3 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

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.4 Sample Problem 4

It can 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

Summary:

It can 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. The pipe of larger diameter alone can fill the pool in 20 hours and the pipe of smaller diameter alone can fill the pool in 30 hours.

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