CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If (a + b)/(a − b) = 9/5 and a, b are positive, then the value of a² : b² is:
The ratio a² : b² is 49 : 4. Applying componendo and dividendo to (a + b)/(a − b) = 9/5 gives a/b = 14/4 = 7/2, and squaring this gives 49/4.
- A49 : 4Correct
- B49 : 25
- C81 : 25
- D14 : 4
Explanation
Componendo and dividendo: 2a/2b = (9+5)/(9−5) = 14/4 = 7/2. So a/b = 7/2 and a² : b² = 49 : 4. Option C squares the given ratio 9/5 directly, which is wrong because that is (a+b)/(a−b), not a/b.
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