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# [Smart Math] Percentages Problem 22

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?

1. 60%
2. 65%
3. 70%
4. 75%
5. 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 = $\frac{300\times 5}{5+4+4+3+4}=\frac{300}{4}=75$

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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