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

**Problem**

**Problem**

$6200 is divided between P, Q, R and S such that Q’s share is 2/3^{rd} of P’s and R’s is 5/6^{th} of Q’s and S’s share is equal to that of Q and R together. What is P’s share?

- $900
- $2500
- $2200
- $1800
- $2000

**The Usual Method**

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*P* : *Q* : *R*

3 : 2

6 : 5

9 : 6 : 5

*S* = 6 + 5 = 11

*P* : *Q* : *R* : *S* = 9 : 6 : 5 : 11

Hence share of *P* = = $1800

**(Ans: 4)**

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

**Using Technique**

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Note that

*P* = 3*x* and *Q* = 2*x*

Hence P’s share = multiple of 3. Only options ‘1’ and ‘4’ are multiples of 3. Thus all other options are eliminated.

Also note from the statement of the question itself that *P* > *Q* > *R* and *S* being *Q* + *R*, may be equal to, or less than or greater than *P*. Thus P’s share is significant.

$900 out of $6200 is not so significant as $1800 out of $6200. Hence $1800 is the share of P.

**(Ans: 4)**

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

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