Which ratio is larger among the following?

3: 7 or 4: 9

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3:7

4:9

both are equal

None

answer is B.

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Detailed Solution

The given ratios are 3:7 and 4: 9
We can write it in fraction form as,

3 : 7 = \frac{3}{7}

4 : 9 = \frac{4}{9}

Now, the LCM of 7 and 9 is 63.
Therefore, multiplying and dividing

\frac{3}{7}

by 9 and

\frac{4}{9}

by 7, we get,

\frac{3 \times 9}{7 \times 9} = \frac{27}{63}

\frac{4 \times 7}{9 \times 7} = \frac{28}{63}

We know that,
28 > 27

\Rightarrow \frac{28}{63} > \frac{27}{63}

\Rightarrow \frac{4}{9} > \frac{3}{7}

\Rightarrow 4 : 9 > 3 : 7

Therefore 3:7 < 4:9.
Hence, the larger ratio is 4:9.
Hence option 2 is correct.

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