Question : Which of the following statements is true? I. $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}=\frac{3}{4}$ II. $\frac{1}{6}+\frac{1}{12}+\frac{1}{20}=\frac{3}{5}$
Option 1: Neither I nor II
Option 2: Only II
Option 3: Only I
Option 4: Both I and II
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Correct Answer: Only I
Solution : Statement I. $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}=\frac{3}{4}$ Consider L.H.S, $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}$ $=\frac{6+2+1}{12}$ $=\frac{9}{12}=\frac{3}{4}=$ R.H.S ⇒ Statement I is correct. Statement II. $\frac{1}{6}+\frac{1}{12}+\frac{1}{20}=\frac{3}{5}$ Consider L.H.S, $\frac{1}{6}+\frac{1}{12}+\frac{1}{20}$ $=\frac{10+5+3}{60}$ $=\frac{18}{60}=\frac{3}{10}\neq$ R.H.S ⇒ Statement II is incorrect. Hence, the correct answer is 'Only I'.
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