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# [Smart Math] Ratio Proportion Problem 9

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

### Problem

Two numbers are in the ratio 5 : 6. When 4 is subtracted from each, the ratio becomes 4 : 5. The greater number is _____?

1. 11
2. 20
3. 24
4. 30
5. 35

### The Usual Method

Since the numbers are in the ratio 5 : 6, the numbers can be 5x and 6 x.

When 4 is subtracted, we get: 5x – 4 and 6x – 4.

Also, $\frac{5x-4}{6x-4}=\frac{4}{5}$

$\therefore \frac{5x-4}{6x-4}=\frac{4}{5}$

$\therefore 25x-20=24x-16$

$\therefore x=4$

Hence the greater number = 6x = 6 x 4 = 24

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.