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? Choose the correct choice from the following options: A) 50 B) 60 C) 10 D) 20 E) 30

Rationale: let us write the fraction for each group of students group a : younger than 10 : 50 % = 50 / 100 = 1 / 2 group b : 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 , b 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 correct answer c
Answer: C