MAT Exam 2021 Paper

Concept:Both wheels are identical in height, so the distance travelled by a wheel is directly proportional to its number of revolutions.The outer wheel follows a larger circle than the inner wheel.Explanation:Let the radius of the inner circle be $r$ m.Then the radius of the outer circle is $(r + 1.22)$ m, because the axle tree is $1.22$ m long.The outer wheel makes $1\frac{1}{2} = \frac{3}{2}$ revolutions for every 1 revolution of the inner wheel.Therefore, the distance travelled by the outer wheel is $\frac{3}{2}$ times the distance travelled by the inner wheel.Thus, we have:$$2\pi(r + 1.22) = \frac{3}{2} \times 2\pi r$$Cancelling $2\pi$ from both sides:$$r + 1.22 = \frac{3}{2}r$$$$r + 1.22 = 1.5r$$$$1.22 = 0.5r$$$$r = 2.44 \text{ m}$$So the radius of the outer circle is:$$r + 1.22 = 2.44 + 1.22 = 3.66 \text{ m}$$Circumference of the circle described by the outer wheel:$$2\pi \times 3.66 = 2 \times \frac{22}{7} \times 3.66 = 23 \text{ m}$$Answer:23 m, i.e., Option B.