CAT 2019 Question Paper | Quants Slot 1

CAT Questions

Here is a classic mensuration question that you can easily answer if you had practiced CAT previous year paper question paper. It is about wheel revolutions and questions of this type have appeared several times in the past. A straightforward application of the formulas and some data manipulation should give the answer. Try cracking this one. If you find it hard, revisit the basics as part of your CAT Preparation journey.

Question 32 : The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was

1. 18π
2. 16π
3. 12π
4. 14π

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Video Explanation

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Explanatory Answer

Circumference of A and B are in the ratio 3: 4
So, Ratio of Distance travelled in one revolution by A and B = 3: 4
Since they travel the same distance,
Ratio of number of revolutions of A and B = 4: 3 ----- (1)
We know that each wheel of A requires 5000 more revolutions than B
So, the Ratio of number of revolutions of A and B = (n + 5000): n ------(2)
So, comparing (1) and (2)
Number of revolutions of A and B are 20000 and 15000 respectively
So, we know Bike B does 15000 revolutions in 45 minutes
Distance travelled = 2 x π x r x Number of revolutions
Speed of Bike B = mph
Speed of Bike B = 2 x x x 5 x 4 Kmph
Speed of Bike B = 16 Kmph

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The question is "The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was"

Hence, the answer is 16π

Choice B is the correct answer.