Question

8) If the ratio of Rate of filling of two Pipes A and B is 3:2. If together they can fill a
Tank 5/6th of Tank in 20 minutes. Then in how many does A alone can fill the
Tank?
(a) 20 min (b) 30 min (C) 40 min (d) 50 min (e) None
​

Answer 1

Answer:

The ratio of rate of filling of two pipes A and B is is given as 3:2.

So, we will take the rate of filling the pipe A as 3x and the rate of filling the pipe B as 2x.

Now, we are given that 5/6th part of tank was filled in 20 minutes.

So, 20 ÷ 5 = 4 minutes were taken by the pipes to fill the 1 part of the tank.

So, the time taken to fill the whole tank is 20 + 4 = 24 minutes.

Now,let us take the part of tank filled by the pipes in minute.

=> 1/3x + 1/2x = 1/24

=> (2x + 3x)/6x² = 1/24

=> 5x = 6x²/24

=> 5x = x²/4

=> 20x = x²

=> x = 20

So, time taken for the pipe A to fill the tank = 2x = 2 × 20 = 40 minutes.

(C) 40 minutes

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Answer 2

${\boxed{\boxed{\mathtt{\red{Answer}}}}}$

Pipe A alone can fill the tank in 40 min .

${\boxed{\boxed{\mathtt{\red{Solution}}}}}$

Given :-

• pipe A and B together in 20 minutes can fill 5/6 th part of tank .
• Ratio of rate of filling of Pipe A and B is 3 : 2 .

Method 1st

→ $\frac{5}{6}$ part is filled in 20 minutes .

So , it means that :-

20 ( 3x + 2x ) = $\frac{5}{6}$

20(5x ) = $\frac{5}{6}$

100x = $\frac{5}{6}$

x = $\frac{5}{6\:\times\: 100}$ = $\frac{1}{120}$

So the time of filling by Pipe A :-

$\frac{120}{3}$ = 40 minutes

___________________

Method 2nd

$\frac{5}{6}$ th part is done in 20 minutes by both pipes . Then total part wi be filled in :-

Both A and B can fill total part of work in $\frac{6}{5}$ × 20

⇝ 24 minutes.

Total capacity of tank is :-

⇝24( 3+2 ) = 120 units

Tank filled by pipe A :-

⇝ $\frac{120}{3}$ = 40 minutes .

${\boxed{\boxed{\mathtt{\red{Answer \: is\: 40\: minutes}}}}}$