Question

Q9. one fill pipe a is 3 times faster than second fill pipe b and takes 32 minutes less than the fill pipe


b. when will the cistern be full if both pipes are opened together?

Answer 1

hello....

(X-32)*3=X*1,

2X= 96, X =48 mins...

A fills in one minute=3/48=16..
B fills in one minute=1/48..

together=1/16 + 1/48=12 mins ...


thank you...

☺

Answer 2

Answer:  The cistern will be be full after 12 minutes if both pipes are opened together.

Step-by-step explanation:

Let the time taken by pipe b to fill the tank = x minutes.

⇒ The work done by pipe a in one minute = 1/x

Since, pipe a is 3 times faster than second fill pipe b,

⇒ The work done by pipe a in one minute = 3/x,

⇒ The time taken by pipe a to fill the tank = x/3

According to the question,

$x - \frac{x}{3}=32$

$\implies \frac{3x-x}{3}=32$

$\implies \frac{2x}{3}=32\implies 2x = 96 \implies x = 48$

⇒ One minute work of pipe a = $\frac{1}{48}$

And, one minute work of pipe b = $\frac{3}{48}$

Hence, the total work done by both pipe in one minute

$=\frac{1}{48}+\frac{3}{48}=\frac{4}{48}=\frac{1}{12}$

⇒ The total time taken by both pipe in entire work when they work simultaneously = 12 minutes.