Question

Arrange the following in increasing order:
(A) 16\(\frac{2}{3}\)%
(B) \(\frac{2}{15}\)
(C) 0.17
(D) 0.25% of 64
Choose the correct answer from the options given below:

• A. B < D < A < C
• B. A < D < B < C
• C. C < D < B < A
• D. A < C < D < B

Answer 1

The Correct Option is A

To arrange the given numbers and expressions in increasing order, we first need to convert each one to a comparable numerical value.

1. (A) \(16\frac{2}{3}\)%: First, convert this mixed number to a fraction or a decimal. \[ 16\frac{2}{3}\% = 16 + \frac{2}{3} = \frac{50}{3}\% = \frac{50}{3} \times \frac{1}{100} = \frac{50}{300} = \frac{1}{6} \approx 0.1667 \]
2. (B) \(\frac{2}{15}\): This is already in fractional form. \[ \frac{2}{15} \approx 0.1333 \] 
3. (C) 0.17: This is in decimal form, so it remains as is, \(0.17\).
4. (D) 0.25% of 64: Calculate this step by step. \[ 0.25\% = \frac{0.25}{100} = 0.0025 \] \[ 0.0025 \times 64 = 0.16 \]

Now we have the following values for comparison:

• (A) \(0.1667\)
• (B) \(0.1333\)
• (C) \(0.17\)
• (D) \(0.16\)

Arrange these in increasing order: \(0.1333 (B) < 0.16 (D) < 0.1667 (A) < 0.17 (C)\).

Thus, the correct order is: \(B < D < A < C\).