Question

Arrange these ratios in ascending order: A. \(1:3\), B. \(1:4\), C. \(2:7\), D. \(3:5\), E. \(5:8\).

• A. \(B<A<C<E<D\)
• B. \(C<A<D<B<E\)
• C. \(B<C<A<D<E\)
• D. \(E<B<A<D<C\)

Hint:

To compare ratios, convert them into fractions or decimals and then arrange.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given five ratios and must arrange them in ascending order (from smallest to largest).

Step 2: Key Formula or Approach:
The easiest and most accurate method to compare ratios is to convert each of them into its equivalent decimal representation.

Step 3: Detailed Explanation:
Let us calculate the decimal value of each ratio:
• A. 1:3 \[ \frac{1}{3} \approx 0.3333 \]
• B. 1:4 \[ \frac{1}{4} = 0.2500 \]
• C. 2:7 \[ \frac{2}{7} \approx 0.2857 \]
• D. 3:5 \[ \frac{3}{5} = 0.6000 \]
• E. 5:8 \[ \frac{5}{8} = 0.6250 \] Comparing these decimal values: \[ 0.2500 < 0.2857 < 0.3333 < 0.6000 < 0.6250 \] Replacing the decimals with their corresponding letters: \[ B < C < A < D < E \]

Step 4: Final Answer:
The ascending order of the ratios is B $<$ C $<$ A $<$ D $<$ E, which corresponds to option (C).