# 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?

$\\ \text{Group A: fraction of students younger than 10:-}\ 50 \%=50 / 100=1 / 2\\ \text{Group B: fraction of students\ 10 years old:-}\ 1/20 \\ \text{Group C: fraction of students older that 10 but younger than 12:-} 1/10\\ \text{Group D: fraction of students 12 years or older:-}\ 70\ students$

$\\ \text{The fraction for group A, B and C together is given by}\ \frac{1}{2}+\frac{1}{20}+\frac{1}{10}==13 / 20\\ \text{The fraction for group D is given by}\ 1-\frac{13}{20}=\frac{7}{20}\\ \text{If x is the total number of students, then}\\ \frac{7}{20}\ of\ x=70 or \frac{7}{20} \times x=70 \Rightarrow x=200$

Students who are 10 years old have a fraction of 1 / 20 of the total x,

So, (1 / 20) of 200 = 10 students

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