Question

In Kendriya Vidyalaya (K.V.), Ujjain, 20% students are athletes. In Navodaya Vidyalaya (N.V.), Ujjain, 25% students are athletes. If N.V. has 60% more students than K.V., then the number of athletes in N.V. is what percent of athletes in K.V.?

• A. 50%
• B. 100%
• C. 200%
• D. 400%

Hint:

In percentage comparison problems, assume a convenient base value (like 100) to simplify calculations and avoid algebra.

Answer 1

The Correct Option is C

Step 1: Assume the total number of students in K.V.
Let the total number of students in Kendriya Vidyalaya be 100.
Step 2: Find the number of athletes in K.V.
Given that 20% of K.V. students are athletes.
\[ \text{Athletes in K.V.} = 20% \text{ of } 100 = 20 \]
Step 3: Find the total number of students in N.V.
N.V. has 60% more students than K.V.
\[ \text{Total students in N.V.} = 100 + 60 = 160 \]
Step 4: Find the number of athletes in N.V.
Given that 25% of N.V. students are athletes.
\[ \text{Athletes in N.V.} = 25% \text{ of } 160 \]
\[ = \frac{25}{100} \times 160 = 40 \]
Step 5: Compare athletes in N.V. with athletes in K.V.
Athletes in K.V. = 20
Athletes in N.V. = 40
Step 6: Find required percentage.
\[ \text{Required percentage} = \frac{40}{20} \times 100 \]
\[ = 200% \]
Step 7: Final conclusion.
Hence, the number of athletes in Navodaya Vidyalaya is 200% of the number of athletes in Kendriya Vidyalaya.