One third of the boys and one half of the girls of a college participate in a…
2023
One third of the boys and one half of the girls of a college participate 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?
Answer: C. 700 — When a fixed fraction of a group's total gives a known count, the group's total is recovered by dividing that count by the fraction — this lets two separate…
- A.
500
- B.
600
- C.
700
- D.
800
Attempted by 1 students.
Show answer & explanation
Correct answer: C
When a fixed fraction of a group's total gives a known count, the group's total is recovered by dividing that count by the fraction — this lets two separate fractional conditions (one for boys, one for girls) be solved independently and then combined.
Let the total number of boys in the college be B and the total number of girls be G.
One third of the boys take part, and this equals the 100 participating boys given in the question, so B/3 = 100, giving B = 300.
The total number of participating students is 300, so the number of participating girls is 300 - 100 = 200.
One half of the girls take part, and this equals the 200 participating girls, so G/2 = 200, giving G = 400.
The total number of students in the college is B + G = 300 + 400 = 700.
Check: one third of 300 boys is 100, and one half of 400 girls is 200; together 100 + 200 = 300 participating students, which matches the number given in the question, confirming the total of 700.