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# [Smart Math] Ratio Proportion Problem 60

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

Two numbers are less than 10 and in the ratio 3 : 1. What is their product?

1. 10
2. 12
3. 14
4. 16
5. 18

### The Usual Method

Let the numbers be 3x and 1x respectively. $x\ne$ any value greater than 3 since for x = 4, 3x will become = 12 which is > 10 and is not allowed as per the question.

Hence x will take values 1, 2 and 3 only.

The product is $3x\times 1x=3x^{2}$

When x =1; $3x^{2}=$3

When x =2; $3x^{2}=$12

When x =3; $3x^{2}=$27

From amongst the above values, only 12 appears in the options, so it is the answer.

(Ans: 2)

Estimated Time to arrive at the answer = 30 seconds.

### Using Technique

Let the numbers be 3x and 1x respectively.

So product of these numbers is $3x\times 1x=3x^{2}$.

Thus the answer should be a multiple of 3 and a perfect square.

Option ‘2’ and ‘5’ are both multiples of 3, but option ‘5’ is not a multiple of a perfect square when it is a multiple of 3. (i.e. 18 $\ne$ 3 x some perfect square). Hence answer is 12.

(Ans: 2)

Estimated Time to arrive at the answer = 5 seconds.
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