Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 31

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

Ratio Proportion


A certain sum of money is divided between A, B and C in the proportion of 2 : 3 : 4. If C were to give B $20, and B were to give A half of what he has now, the amounts which A and C have now would be same. What is the amount divided between the three?

  1. $420
  2. $480
  3. $500
  4. $540
  5. $600

The Usual Method

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Let the shares of A, B and C be 2x, 3x and 4x respectively. (where ‘x’ is the constant of proportionality)


(4x – 20) is the new share of C

\frac{3x+20}{2} is the new share of B and

2x + \frac{3x+20}{2} is the new share of A.

Also, since new shares of A and C are equal:

2x + \frac{3x+20}{2} = (4x – 20)

\therefore 2x+1.5x+10=4x-20

\therefore 3.5x+10=4x-20

\therefore 0.5x=30

\therefore x=60

Hence total sum = 2x+3x+4x=9x=9\times 60= $540

(Ans: 4)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Total sum of money to be shared = 2x+3x+4x=9x. Hence the sum should be a multiple of 9. Only option ‘4’ ($540) is a multiple of 9. This eliminates all the other options, so option ‘4’ is the answer.

(Ans: 4)

Estimated Time to arrive at the answer = 5 seconds.

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