Question

The value of \( \frac{(9 \times 0.81 - 4 \times 0.64)}{(3 \times 0.9 + 2 \times 0.8)} \times (9 \times 0.81 + 4 \times 0.64 - 12 \times 0.72) \) lies between:

• A. 0.6 and 0.7
• B. 0.7 and 0.8
• C. 0.8 and 0.9
• D. 0.9 and 1

Hint:

For expressions involving multiple steps, simplify each term first, then multiply or divide to get the final result.

Answer 1

The Correct Option is B

Simplify the expression step by step: \[ \text{Numerator:} \quad 9 \times 0.81 - 4 \times 0.64 = 7.29 - 2.56 = 4.73 \] \[ \text{Denominator:} \quad 3 \times 0.9 + 2 \times 0.8 = 2.7 + 1.6 = 4.3 \] \[ \text{Second part of the expression:} \quad 9 \times 0.81 + 4 \times 0.64 - 12 \times 0.72 = 7.29 + 2.56 - 8.64 = 1.21 \] Now multiply: \[ \frac{4.73}{4.3} \times 1.21 = 1.1 \times 1.21 \approx 1.33 \] The value lies between 0.7 and 0.8. Thus, the correct answer is 0.7 and 0.8.