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[Smart Math] Ratio Proportion Problem 30

Here’s and example of a SMART MATH problem for 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

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

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’).