Here’s and example of a SMART MATH problem for PERCENTAGES.
Problem
In a examination of 5 subjects, all with the same maximum score, a candidate scored 60% in the aggregate and marks in proportion to 5 : 4 : 4 : 3 : 4 in individual subjects. What was his highest score in any subject?
- 60%
- 65%
- 70%
- 75%
- 80%
The Usual Method
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Assuming that the maximum marks in a subject is 100, hence average marks in 5 subject = 60
Hence total marks in 5 subjects = 60 x 5 = 300.
Maximum marks will be that whose proportion is ‘5’ from 5 : 4 : 4 : 3 : 4.
Hence maximum marks =
Hence percentage marks = 75%
(Ans: 4)
Estimated Time to arrive at the answer = 45 seconds.
Using Technique
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Simple observing 5 : 4 : 4 : 3 : 4 we notice that the average of 5, 4, 4, 3 and 4, is 4.
Hence, 4 corresponds to the average of 60% and so 5 will correspond to the average of 75% (using cross multiplication).
(Ans: 4)
Estimated Time to arrive at the answer = 10 seconds.
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