Exams › SSC CGL (Prelims) › General

Evaluate: \(\dfrac{0.5 \times 0.5 \times 0.5 + 0.01 \times 0.01 \times 0.01}{1.5 \times 1.5 \times 1.5 + 0.03 \times 0.03 \times 0.03}\).

1. 1/9
2. 1/81
3. 1/27
4. 1/3

Correct answer: 1/27

Solution

The numerator is \(0.5^3 + 0.01^3 = \frac{1}{8} + \frac{1}{1000000}\), and the denominator is \(1.5^3 + 0.03^3 = \frac{27}{8} + \frac{27}{1000000}\). Factoring the common structure gives a ratio of \(\frac{1}{27}\). Hence the value is \(1/27\).

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