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

**Problem**

**Problem**

$ 190 is divided between A, B and C, so that A’s share is times B’s and B’s is times that of C’s. What is C’s share?

- 90
- 60
- 40
- 30
- 20

**The Usual Method**

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A’s share = 1.5 times B’s

A : B = 1.5 : 1

Also B’s share = 1.5 times C’s

B: C = 1.5 : 1

A : B : C = 1.5 : 1

aaaaaaaaaaaaaaaaaaaaaaaaaa 1.5 : 1

= 2.25 : 1.5 : 1

Hence C’s share =

**(Ans: 3)**

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

**Using Technique**

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Partially ignoring the relationship between A, B and C, we can assume that A and B are both 1.5 times C. Hence, total proportion = 1.5 + 1.5 + 1 = 4

But in reality, A is 1.5 times B. Hence the value of C has to be little less than 45. From amongst the options 40 is the only value that satisfies the condition.

**(Ans: 3)**

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

Note: In the event of the options being close to 45 and less than that, just substitute the values as follows:

40 x 1 = 40

40 x 1.5 = 60

60 x 1.5 = 90

Sum: 40 + 60 + 90 = 190, which satisfies the conditions, so option ‘3’ is the answer.

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