IIFT 2018 Question Paper | Quants

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 2018 IIFT, Quants was 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 13 : A metallic solid is made up of a solid cylindrical base with a solid cone on its top. The radius of the base of the cone is 5 cm. and the ratio of the height of the cylinder and the cone is 3:2. A cylindrical hole is drilled through the solid with height equal to 2/3^rd of the height of solid. What should be the radius (in cm) of the hole so that the volume of the hole is 1/3^rd of the volume of the metallic solid after drilling?

1. \\sqrt{\frac{45}{8}})
2. \\sqrt{\frac{35}{8}})
3. \\sqrt{\frac{65}{8}})
4. \\sqrt{\frac{55}{8}})

Explanatory Answer

Let the height of the cylinder be 3h and the height of the cone be 2h
Volume of the total solid = Π x 5² x 3h + (1/3) x Π x 5² x 2h
= 75Πh + (50/3)Πh = (275/3)Πh
Height of drilling = (2/3) x 5h = 10h/3
Volume of hole = Π x r² x 10h/3
\\frac{\text { Volume of hole }}{\text { Volume of solid-volume of hole }}) = \\frac{1}{3})
Solving we get r = \\sqrt{\frac{55}{8}}) 

The answer is '\\sqrt{\frac{55}{8}})'

Choice D is the correct answer.