There are multiple ways of doing this. Let's solve this using two method:
Method 1:We need to find the value of c:a and we know that
a:b = 2:3 => \(\frac{a}{b}\) = \(\frac{2}{3}\) ...(1)
b:c = 5:7 => \(\frac{b}{c}\) = \(\frac{5}{7}\) ...(2)
Multiplying (1) and (2) we get
\(\frac{a}{b}\) * \(\frac{b}{c}\) = \(\frac{2}{3}\) * \(\frac{5}{7}\)
=> \(\frac{a*b}{b*c}\) = \(\frac{2*5}{3*7}\)
=> \(\frac{a}{c}\) = \(\frac{10}{21}\)
Taking inverse on both the sides we get
\(\frac{c}{a}\) = \(\frac{21}{10}\)
So, Answer will be E
Hope it helps!
Method 2:a:b = 2:3 and b:c = 5:7
b is the common variable in both the ratios
so, lets try to make value of b same on the right hand side for both the ratios
b corresponds to 3 in a:b = 2:3 and
b corresponds to 5 in b:c = 5:7
So, we can make the value of b common by taking LCM(3,5) which is 15
[IF you need a refresher on LCM and GCD then check out
this post.]
a:b = 2:3 = 2*5 : 3*5 = 10:15
b:c = 5:7 = 5*3 : 7*3 = 15:21
So, a:c = 10:21
=> c:a = 21:10
So, Answer will be E
Hope it helps!