Which of the ratios given below is the greatest among them?

Question

Which of the ratios given below is the greatest among them?

1. A. 5 : 8
2. B. 3 : 5
3. C. 7 : 11 (Correct answer)
4. D. 4 : 7

Correct Answer

Option C — 7 : 11

Detailed Solution & Explanation

The correct answer is 7 : 11.

Shortcut Trick

• Convert each ratio to a decimal and compare directly — with four small ratios this is faster than any cross-multiplication scheme.
  • $5 : 8 = 0.625$
  • $3 : 5 = 0.600$
  • $\mathbf{7 : 11 = 0.636}$
  • $4 : 7 \approx 0.571$
• The largest is 7 : 11.

Alternate Method

• Cross-multiplication between the two leading candidates: for $\dfrac{5}{8}$ versus $\dfrac{7}{11}$, compare $5 \times 11 = 55$ against $7 \times 8 = 56$.
• Since $56 > 55$, $\dfrac{7}{11} > \dfrac{5}{8}$, and $\frac{5}{8}$ already beat the other two.

Additional Information

• Cross-multiplication rule: for positive fractions, $\dfrac{a}{b} > \dfrac{c}{d}$ exactly when $ad > bc$. It avoids decimals entirely and never rounds.
• A common LCM of the denominators also works: over 440, the fractions are $\frac{275}{440}$, $\frac{264}{440}$, $\frac{280}{440}$ and $\frac{251.4}{440}$ — again 7:11 leads.
• Beware the instinct that a bigger numerator means a bigger ratio; $\frac{7}{11}$ beats $\frac{5}{8}$ by a margin of less than 0.012, so estimation alone is unsafe here.