One-third of the boys and one-half of the girls of a college participated in a social work project. If the number of participatin…

Question

One-third of the boys and one-half of the girls of a college participated in a social work project. If the number of participating students is 300 out of which 100 are boys, what is the total number of students in the college?

1. A. 500
2. B. 600
3. C. 700 (Correct answer)
4. D. 800

Correct Answer

Option C — 700

Detailed Solution & Explanation

The correct answer is 700.

Key Points

• Of the 300 participants, 100 are boys, so 200 are girls.
• One-third of the boys participated, so total boys = 100 × 3 = 300.
• One-half of the girls participated, so total girls = 200 × 2 = 400.
• Total students = 300 + 400 = 700.

Additional Information

• The efficient route is to work backwards from the participants to the totals, rather than setting up simultaneous equations in the unknown totals.
• Always substitute the answer back as a check: with 300 boys and 400 girls, one-third of 300 is 100 and one-half of 400 is 200, giving the stated 300 participants against a college strength of 700.
• Questions of this shape recur with different fractions, so the method matters more than the numbers.