Question

Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is

Answer 1

Correct Answer: 52

Step 1: Define variables 

Let:

• \( h \) = students studying only H
• \( e \) = students studying only E
• \( x \) = students studying only H and P but not E
• \( y \) = students studying only E and P but not H

Given:

• Only P = 0
• All three subjects = 10
• Only H and E but not P = 20

Step 2: Equating total H and E counts

Number of students studying H: \[ H = h + x + 20 + 10 \] Number of students studying E: \[ E = e + y + 20 + 10 \] Given \( H = E \), we have: \[ h + x = e + y \]

Step 3: Total students

Total students: \[ h + x + 20 + 10 + e + y = 74 \] Substitute \( h + x = e + y \): \[ (h + x) + (e + y) + 30 = 74 \] \[ (h + x) + (h + x) = 44 \] \[ 2(h + x) = 44 \] \[ h + x = 22 \]

Step 4: Number studying H

\[ H = (h + x) + 20 + 10 = 22 + 20 + 10 = 52 \]

✅ Final Answer: The number of students studying H = 52