Question

In a group of students 50% like tea 70% like coffee 10% dont like both and 120 like both. Find the number of students

Answer 1

Answer:

400 students

Step-by-step explanation:

Let total students be x

no . of students like tea=50/100×x=x/2

no.of students like coffee=7x/10

no.of students dont like both = x/10

students liking both= 120

A.T.Q

$\frac{x}{2} + \frac{7x}{10} + \frac{x}{10} + 120 = x \\ \frac{5x + 7x + x}{10} = x \\ \frac{13x}{10} + 120 = x \\ \frac{13x}{10} - \frac{x}{1} = - 120 \\ \frac{3x}{10} = - 120 \\ 3x = 120 \times 10 = 1200 \\ x = \frac{1200}{3} \\ = 400students$