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# [Smart Math] Ratio Proportion Problem 8

Here’s and example of a SMART MATH problem for RATIO PROPORTION.

### Problem

If 5a = 7b and 3b = 11c, find a : b : c

1. 5 : 7 : 3
2. 55 : 77 : 15
3. 15 : 55 : 77
4. 11 : 7 : 3
5. 77 : 55 : 15

### The Usual Method

5a = 7b

$\therefore \frac{a}{b}=\frac{7}{5}$

Similarly, if 3b = 11c

$\therefore \frac{b}{c}=\frac{11}{3}$

$\therefore$      a          :           b          :           c

aaaaaa7          :           5

aaaaaaaaaaaaaaa 11        :           3

=          77        :           55        :           15

(Ans: 5)

Estimated Time to arrive at the answer = 30 seconds.

### Using Technique

Since ‘2’ is common in both the relationships, simply find the product of coefficients of ‘1’ and ‘3’ i.e. 5 x 11 = 55 which will be the corresponding term for ‘2’. This eliminates all options other than ‘3’ and ‘5’.

If 3b = 11c, it means that ‘3’ is smaller than ‘2’, Hence in a : b : c, if the corresponding figure for ‘2’ is 55, ‘3’ should be less than 55. This is true only for option ‘5’.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds.
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