In a certain school, 20% of students are below 8 years of age. The number of…
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In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?
Answer: C. 100 — Concept: When a population is split into age-based percentage groups, the size of the whole can be recovered once one combined group's actual count and its…
- A.
72
- B.
80
- C.
100
- D.
120
Attempted by 9 students.
Show answer & explanation
Correct answer: C
Concept:
When a population is split into age-based percentage groups, the size of the whole can be recovered once one combined group's actual count and its percentage share of the total are both known: Total = (count in that share) ÷ (percentage as a decimal).
Application:
20% of students are below 8 years, so the remaining 80% are 8 years old or above.
The number of students exactly 8 years old is given as 48.
The number of students above 8 years is 2/3 of that group: 2/3 × 48 = 32.
Together, students who are 8 years old or above = 48 + 32 = 80, and this count represents the 80% share found in step 1.
Let the total number of students be x. Then 80% of x = 80, so x = 80 ÷ 0.8 = 100.
Cross-check:
With a total of 100 students: 20% (20 students) are below 8 years, and the remaining 80 students are 8 years or older — 48 exactly 8 years old and 32 (which is 2/3 of 48) above 8 years, since 48 + 32 = 80. Every given ratio checks out.