Ratio A=1/20
Ratio B= 1/30
Combined ratio= 1/20+1/30=1/12

Now, since we know that tap A was opened before B, we can create the function:

1/20*x + 1/12*(15-x)=1

Substitute the values and you'll find that the correct answer is B.
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hey GMATinsight
Why did you take 60 as total work done ? i guess its LCM of 20 and 30, but then let me ask you a question isnt in denominator given time 1/20 where 1 is work and 20 is time
thank you

Hey No, I don't think so: the reasoning behind the equation is this:

1)\(1/20x\) Is the ratio of A * time it is activated
2)\(1/12*(15-x)\) Is the ratio after you open tap B, which working together with tap A gives a combined ratio of 1/12, *time they are activated together(i.e. total time - x = 15-x).
3)Equate their sum to 1, which is the cistern we have to fill.

Then solve the equation and the result will be \(15/2\), hence the correct answer is B.

I learned to create models in high school and university, I just applied this knowledge to this work and rate problem I'm sure there are other ways, but that's the one that came up in my mind at the moment.

If you need any further clarification just quote me and I'll be happy to help
And please, give kudos if you found this solution helpful
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hey Italiandrummer97

thank you ! got it now! happy international drumming day!

\(\frac{x}{20} +\frac{15-x}{12} = 1\)

\((60)(\frac{x}{20} +\frac{15-x}{12}) = 1(60)\)

\(3x+5(15-x) =60\)

\(3x+75-5x=60\)

\(15=2x\)

\(x = 7.5\)

Solution

Given:

• Two taps can fill a cistern in 20 minutes and 30 minutes.
• First tap was opened initially for x minutes.
• After first x minutes, both the taps were open.

To find:

• The value of x

Approach and Working out:

Let us take the capacity of cistern= LCM(20, 30)=60 litres.

Hence, Tap A fills the 3 litres in 1 min

• And, Tap B fills the 2 litres in 1 min.

Thus, for first x min, the capacity of cistern filled = 3x
After, x min, both the taps were open for (15-x) min.

• Therefore, the amount filled by both the taps=5*(15-x)= 75-5x

Now, the cistern got filled.

• Hence, 3x+75-5x= 60
• 2x= 15
• x= 7.5 min

Answer: B
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