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# [Smart Math] Ratio Proportion Problem 31

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

### Problem

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

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

Thus,

(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 [contentblock id=google-adsense-post] 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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