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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 42

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

Ratio Proportion

Problem

If the shares of A and B are in the ratio \frac{1}{2}:\frac{1}{3} and also, it is equal to that of B and C. What is the proportion in which profit is divided between A, B and C?

  1. 1 : 2 : 3
  2. 3 : 2 : 6
  3. 6 : 5 : 9
  4. 2 : 3 : 4
  5. 9 : 6 : 4

The Usual Method

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A : B = \frac{1}{2}:\frac{1}{3} = B : C

\therefore A : B = 3 : 2 = B : C

\therefore       A         :           B         :           C

3          :           2

3          :           2

9          :           6          :           4

Hence answer is 9 : 6 : 4.

(Ans: 5)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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Note that \frac{1}{2}:\frac{1}{3} is the same as 0.5 : 0.33.

Since 0.5 > 0.33, share of A > B and B > C

\therefore A > B > C. From amongst the options, only option ‘5’ satisfies this condition. Hence answer is 9 : 6 : 4.

(Ans: 5)

Estimated Time to arrive at the answer = 5 seconds.
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