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?
- 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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