In the town of Unevenville, it is a tradition to have the size of the front…
2026
In the town of Unevenville, it is a tradition to have the size of the front wheels of every cart different from that of the rear wheels. They also have special units to measure cart wheels which is called uneve. The circumference of the front wheel of a cart is 133 uneves and that of the back wheel is 190 uneves. What is the distance travelled by the cart in uneves, when the front wheel has done nine more revolutions than the rear wheel?
- A.
5700
- B.
3990
- C.
1330
- D.
3998
Attempted by 10 students.
Show answer & explanation
Correct answer: B
Concept: For a wheel of circumference C, the number of revolutions it makes while covering a distance d is Revolutions = d / C. When two wheels of different circumferences cover the SAME distance, the one with the smaller circumference makes more revolutions — the gap between their revolution counts depends on the common distance and the two circumferences.
Application:
Let the distance travelled be d uneves.
Front wheel (circumference 133): revolutions = d/133. Rear wheel (circumference 190): revolutions = d/190.
The front wheel makes 9 more revolutions than the rear wheel: d/133 − d/190 = 9.
Combine the fractions over the common denominator 133 × 190: d(190 − 133)/(133 × 190) = 9, i.e., 57d = 9 × 133 × 190.
Solve for d: d = (9 × 133 × 190)/57 = 227430/57 = 3990.
Cross-check: At d = 3990 uneves, the front wheel makes 3990/133 = 30 revolutions and the rear wheel makes 3990/190 = 21 revolutions; the difference is 30 − 21 = 9, matching the given condition. So the distance travelled by the cart is 3990 uneves.