Question

In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

• A. \(5.4\) m
• B. \(5\) m
• C. \(6\) m
• D. \(4\) m
• E. \(4.4\) m

Answer 1

The Correct Option is C

Concept: Race ratios:

• If A beats B by 10 m in 100 m, then

\[ A:B = 100:90 = 10:9 \] \[ A:C = 100:87 \]
Step 1: Find B:C ratio.
\[ \frac{B}{C} = \frac{B/A}{C/A} = \frac{9/10}{87/100} = \frac{9 \times 100}{10 \times 87} = \frac{900}{870} = \frac{30}{29} \]
Step 2: Apply for 180 m race.
When B runs 180 m: \[ C = 180 \times \frac{29}{30} = 174 \]
Step 3: Difference.
\[ 180 - 174 = 6 \text{ m} \]
Step 4: Option analysis.

• (A) Incorrect $\times$
• (B) Incorrect $\times$
• (C) Correct \checkmark
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (C).