[Smart Math] Ratio Proportion Problem 34

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

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?

1. 90
2. 60
3. 40
4. 30
5. 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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