Arrange the given ratios in descending order:

a. 7 : 15

b. 15 : 23

c. 17 : 25

d. 21 : 39

Choose the correct answer from the options given below

c > b > d > a

Here, we follow some rules to find small or big fractions:

i. Make the numerator of two fractions equal and whose denominator value is small that fraction would be large and whose denominator value is big that fraction value will be small.

ii.  Make the denominator of two fractions equal and whose numerator value is small that fraction would be small and whose numerator value is big that fraction value will be big.

iii. Cross multiply the two fractions, whose numerator is big that fraction gives the higher value.

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Now, According to question, given fractions are:

a. 7 : 15 = \(\frac{7}{15}\)

b. 15 : 23 = \(\frac{15}{23}\)

c. 17 : 25 = \(\frac{17}{25}\)

d. 21 : 39 = \(\frac{21}{39}\)

Now, lets make numerator of a, b and d equal, we get

a. \(\frac{7}{15}\) = \(\frac{105}{225}\)

b. \(\frac{15}{23}\) = \(\frac{105}{161}\)

d. \(\frac{21}{39}\) = \(\frac{105}{195}\)

Here, according to rule 1, b > d > a ................(i)

Now, cross multiple b. and c., we get

b. : c. = \(\frac{15}{23}\) : \(\frac{17}{25}\) = 375 : 391

Hence, c > b    .....................(ii)

From (i) and (ii), we can say,

c > b > d > a