IIFT 2019 Question Paper | Quants

CAT Questions

The best way to boost your IIFT prep is to practice the actual IIFT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. In the 2019 IIFT, quants were a mixed bag of questions of varying difficulty, with some routine questions and the others were very demanding. Some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts.

Question 12 : Rohit purchased a cistern which had a leakage. The cistern can be filled by two inlet pipes, which can individually fill the cistern in 12 min and 15 min respectively. Despite leakage, the two inlet pipes together can fill the cistern in 20 min. How long will it take to empty the completely full the cistern due to leakage?

---

---

Video Explanation

---

---

Explanatory Answer

The cistern has 2 inlet pipes P₁ and P₂ and a Leakage L. The total flow out of these three pipes gives the net flow.
It is given that pipes P₁ and P₂ fill the tank in 12 and 15 minutes respectively.

So, in 1 minute P₁ will fill \\frac{1}{12}) ^th of the tank.

And in 1 minute P₂ will fill \\frac{1}{15}) ^th of the tank.

The total flow in 1 minute will be \\frac{1}{20}) ^th of the tank.

Lets say the L is \\frac{1}{L}). Because it is emptying the cistern, we take it as negative.

Then,
\\frac{1}{12}) + \\frac{1}{15}) - \\frac{1}{L}) = \\frac{1}{20})

\\frac{5}{60}) + \\frac{4}{60}) - \\frac{3}{60}) = \\frac{1}{L})

\\frac{1}{10}) = \\frac{1}{L}) Which means that the Leaking pipe empties 1/10^th each minute and so, the completely filled cistern is emptied in 10 minutes.

---

The question is "How long will it take to empty the completely full the cistern due to leakage?"

Hence, the answer is, "10"