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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 43

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

Ratio Proportion

Problem

A profit of $13,000 is to be divided among A, B, C and D. What is A’s share, if A : B = 3 : 2, B : C = 3 : 2 and C : D = 3 : 2?

  1. $4500
  2. $5400
  3. $3600
  4. $1600
  5. $2400

The Usual Method

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A         :           B         :           C

3          :           2

3          :           2

9          :           6          :           4

So,
A         :           B         :           C         :           D

9          :           6          :           4

3          :           2

27        :           18        :           12        :           8

\therefore 27x+18x+12x+8x=65x = 13000 (Where ‘x’ is the constant of proportionality)

\therefore x=\frac{13000}{65}=200

\therefore A’s share = 27x=27\times 200 = $5400

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Using the rule explained in the section of Proportion in Stuff to Remember, we can directly write:

A : B : C : D = 27 : 18 : 12 : 8

We also know that share of A = 27x

Hence, the answer should be a multiple of 27. Hence option ‘2’.

(Ans: 2)

Estimated Time to arrive at the answer = 10 seconds.
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