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

**Problem**

**Problem**

In what proportion must a number be divided so that 1/3^{rd} of the first part and 1/8^{th} of the second part are together equal to 1/4^{th} of the number?

- 6 : 8
- 6 : 4
- 2 : 3
- 1 : 4
- 5 : 4

**The Usual Method**

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Let the two parts be ‘*x*’ and ‘*y*’.

Hence,

**(Ans: 2)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Since, the first part has to be divided by 3 (1/3^{rd} of first part), it should be either 3 or a multiple of 3.

Similarly the second part has to be divided by 8 (1/8^{th} of second part), so it should be some multiple of 2 (prime factor of 8).

You will observe that only options ‘1’ and ‘2’ satisfy these conditions. Now taking option ‘1’, we verify it as follows:

Reduce 6 : 8 to 3 : 4 first

where ‘*k*’ is the constant of proportionality

But 1.5*k* is not 1/4^{th} of 7*k*. Hence this option does not satisfy.

Similarly taking option ‘2’ we verify it as follows:

Reduce 6 : 4 to 3 : 2 first

Total number is = 3*k* + 2*k* = 5*k*

1.25*k* = 1/4^{th} of 5*k*. Hence it satisfies.

**(Ans: 2)**

*Estimated Time to arrive at the answer = 15 seconds.*

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