if \(\rm \frac{2a-5}{a}-\frac{4b-5}{b}+\frac{6c+5}{c}=0\), What is the value of \(\rm \left(\frac{1}{a}-\frac{1}{b}-\frac{1}{c}\right)\) ?

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Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 2)

Answer 1

Calculation:

We have,

\(\rm \frac{2a-5}{a}-\frac{4b-5}{b}+\frac{6c+5}{c}=0\)

⇒ 2 - \(\frac{5}{a}\) - 4 + \(\frac{5}{b}\) + 6 + \(\frac{5}{c}\) = 0

⇒ 8 - 4 = \(\frac{5}{a}\) - \(\frac{5}{b}\) - \(\frac{5}{c}\)

⇒ 4 = 5 [\(\frac{1}{a}\) - \(\frac{1}{b}\) - \(\frac{1}{c}\) ]

⇒ [\(\frac{1}{a}\) - \(\frac{1}{b}\) - \(\frac{1}{c}\) ] = 4/5

∴ The correct answer is option (1).

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