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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 9

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

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

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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.

Using Technique

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Of 5x and 6x, the greater is 6x, which means that it is a multiple of 6. Thus all options other than ‘3’ and ‘4’ are eliminated as they are not multiples of 6. Also, when that number is to be subtracted by 4, it should yield a number which is a multiple of 5 since the ratio after subtraction changes to 4 : 5.

24 – 4 = 20 is a multiple of 5 but 30 – 4 = 26 is not a multiple of 5 and hence 24 is the number and option ‘3’ is the answer.

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds.
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