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# [Smart Math] Ratio Proportion Problem 38

Here’s and example of a SMART MATH problem for 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 $\frac{2}{3}s=\frac{3}{4}a=\frac{3}{5}c$; 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.
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