Question

In a certain school, 25% of students are below 10 years of age. The number of students above 10 years of age is 3/5 of the number of students of 10 years of age, which is 75. What will be the total number of students in the school?

• A. 120
• B. 135
• C. 160
• D. 180

Hint:

In percentage problems, always set up the equation based on the total number and the percentage breakdowns. Solving the equation will give you the required quantity.

Answer 1

The Correct Option is C

Let the total number of students be \( N \). Step 1: Set up the relations.
25% of the students are below 10 years of age, which is \( \frac{25}{100} \times N = \frac{N}{4} \).
The number of students of 10 years of age is given as 75.
The number of students above 10 years of age is \( \frac{3}{5} \times 75 = 45 \).

Step 2: Find the total number of students. The total number of students is the sum of the students below 10 years, students of 10 years, and students above 10 years: \[ \frac{N}{4} + 75 + 45 = N \] Simplifying: \[ \frac{N}{4} + 120 = N \] \[ 120 = N - \frac{N}{4} \] \[ 120 = \frac{3N}{4} \] \[ N = \frac{120 \times 4}{3} = 160 \] Thus, the total number of students in the school is 160. Final Answer: The correct answer is (c) 160.