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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 38

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

Ratio Proportion

Problem

The total number of students in a college is 270. If 2/3rd of the number of students in the Science stream is same as 3/4th of the number of students in the Arts stream and 3/5th of the number of students in the Commerce stream, how many are Science students?

  1. 70
  2. 80
  3. 90
  4. 100
  5. 110

The Usual Method

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\frac{2}{3}s=\frac{3}{4}a=\frac{3}{5}c; where, ‘s’ = number of Science students, ‘1’ = number of Arts students and ‘3’ = number of Commerce students.

Also s+a+c=270

From \frac{2}{3}s=\frac{3}{4}a, we get:

\frac{s}{a}=\frac{3}{4}\times \frac{3}{2}=\frac{9}{8}

From \frac{3}{4}a=\frac{3}{5}c, we get:

\frac{a}{c}=\frac{3}{5}\times \frac{4}{3}=\frac{4}{5}=\frac{8}{10}

\therefore s:a:c=9:8:10

\therefore s=\frac{9}{27}\times 270=90

(Ans: 3)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Note that 2/3rd of Science students should be a natural number since number of students cannot be a fraction. Hence, number of Science students must be divisible by 3. The only option divisible by 3 is option ‘3’ i.e. 90 students.

(Ans: 3)

Estimated Time to arrive at the answer = 5 seconds.
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