If a:b = 2:3 and b:c = 5:7, what is c:a?

Question

If a:b = 2:3 and b:c = 5:7, what is c:a?​

A. 2:7​

B. 3: 7​

C. 7:2​

D. 10: 21​

E. 21:10​

Nipungupta9081 · Answer

A/B = 2/3 
B = 3A/2

B/C = 5/7 putting value of B 
3A/C * 1/C = 5/7

A/C = 21:10
Answer E

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yashikaaggarwal · Answer

If a:b = 2:3 and b:c = 5:7, what is c:a?​
A:B:C
2:3:_ * multiply by 5
 _:5:7 * multiply by 3

10:15:21
A:C = 10:21
C:A = 21:10

Answer is E

BrushMyQuant · Answer

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
 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!

If a:b = 2:3 and b:c = 5:7, what is c:a?

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If a:b = 2:3 and b:c = 5:7, what is c:a?​

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If a:b = 2:3 and b:c = 5:7, what is c:a?