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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 30

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

Ratio Proportion

Problem

A man divides his property in such a way that his first three sons get \frac{1}{4}, \frac{1}{2} and \frac{1}{6} of the property respectively and the fourth son gets the remainder amount of $2000. What was the whole property worth?

  1. $14000
  2. $16000
  3. $20000
  4. $24000
  5. $30000

The Usual Method

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Let the worth of the whole property be ‘x’.

Hence the shares of the first three sons will be: \frac{1}{4}x, \frac{1}{2}x and \frac{1}{6}x respectively.

Hence remaining property after dividing it among the first three sons is:

x-\left( \frac{1}{4}x+\frac{1}{2}x+\frac{1}{6}x \right) = $2000

\therefore 12x-3x+6x+2x=24000

\therefore x= $24000

(Ans: 4)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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Observe that the property needs to be divided into \frac{1}{4}, \frac{1}{2} and \frac{1}{6} parts. This means that the property is divisible by 2, 4 and 6 i.e. 12 (LCM of 2, 4 and 6). Hence the property is divisible by 12. The only option that is divisible by 12 is $24000 (option ‘4’).

(Ans: 4)

Estimated Time to arrive at the answer = 5 seconds.
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