Which of the following is the smallest ratio?

\(\frac{5}{6}, \frac{7}{9}, \frac{11}{12}, \frac{13}{18} \)

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SSC CGL 2023 Tier-I Official Paper (Held On: 27 Jul 2023 Shift 1)
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  1. \(\frac{7}{9} \)
  2. \(\frac{13}{18}\)
  3. \(\frac{5}{6}\)
  4. \(\frac{11}{12}\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{13}{18}\)
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Detailed Solution

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Calculations:

5/6 = 0.8333

7/9 = 0.7778

11/12 = 0.9167

13/18 = 0.7222

⇒ The smallest decimal equivalent is for 13/18

∴ The smallest ratio among the given options is 13/18.

Alternate Method \(\frac{5}{6}, \frac{7}{9}, \frac{11}{12}, \frac{13}{18} \)

LCM of 6, 9, 12, and 18 = 36

Now the fraction becomes

5/6 = 30/36

7/9 = 28/36

11/12 = 33/36

13/18 = 26/36

Now, compare and find the smallest numerator

Smallest = 26/36 = 13/18

∴ The smallest ratio among the given options is 13/18.

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