Discussion
In a college survey, 3/16 students said that they prefer online method to pay their mobile bills, 5/8 said they prefer to go to a mobile shop for the bill payment. The remaining 75 students said they had no clear choice. How many students preferred online method and what is the total number of students?
Answer: A
The answer is 75 students preferred online payment, out of 400 in total.
The online and shop groups together are \(\tfrac{3}{16} + \tfrac{5}{8} = \tfrac{3}{16} + \tfrac{10}{16} = \tfrac{13}{16}\) of the students, so the 75 undecided students are the remaining \(\tfrac{3}{16}\).
\[ \begin{aligned} \tfrac{3}{16}N &= 75 \Rightarrow N = 400 \\ \text{online} &= \tfrac{3}{16} \times 400 = 75 \end{aligned} \]
The online group happens to equal the undecided group, both 3/16 of 400. A total of 300 does not make 3/16 of it equal to 75, and 150 online students would be 3/8 of 400, not 3/16.
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