Question

If front and rear wheels of a vehicle make 10 and 20 revolutions respectively to cover the same distance, then what is ratio of the circumferences of the two wheels?

• A. 2:1
• B. 4:1
• C. 1:4
• D. 1:3

Answer 1

The Correct Option is A

Finding the Ratio of the Circumferences of the Front and Rear Wheels 

Step 1: Define Variables

Let the circumference of the front wheel be \( C_1 \) and that of the rear wheel be \( C_2 \).

Step 2: Use the Distance Formula

The total distance covered by each wheel is the same, given by:

\[ \text{Revolutions} \times \text{Circumference} = \text{Same Distance} \]

Step 3: Set Up the Equation

\[ 10 \times C_1 = 20 \times C_2 \]

Step 4: Solve for the Ratio

Dividing both sides by \( 10C_2 \):

\[ \frac{C_1}{C_2} = \frac{20}{10} \]

\[ = 2:1 \]

Final Answer:

Thus, the correct answer is 2:1 (Option A).