In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?  Answers:
A) 5
B) 10
C) 15
D) 20
E) 25
Solution   Let us write the fraction for each group of students   Group A: younger than 10: 50% = 50/100 = 1/2   Group 10: 10 years old: 1/20   Group C: older that 10 but younger than 12: 1/10   Group D: 12 years or older: 70 students   The fraction for group A, 10 and C together is given by   1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator   = 13 / 20 , add numerators   The fraction for group D is given by   20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students   If X is the total number of students, then   7 / 20 of X = 70   or (7 / 20) × X = 70   Solve for X   X = 70 × (20 / 7) = 200   Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to   (1 / 20) of 200 = 10 students   ANSWER IS 10
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In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?