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

- 18π
- 16π
- 12π
- 14π

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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

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" **

**Choice B** is the correct answer.

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