Question

1) In a class 2/5 of the students like cricket, 2/7 of the students like hockey and the rest of the students like football. If 11 students liked football and if each student liked only one game, find the number of students liked cricket and also the total number of students in the class.


2)If 6 more than a number is doubled it becomes equal to 4 less than three times the number. Find the number.

Answer 1

1)
Let the total number of students be X
students liking football = { 1 - (2/5 + 2/7) } * X
= { 1 - (24/35) } * X
= { 11/35 } * X
= 11X / 35
Given that, the number of students liking football is 11
So, 11X / 35 = 11
11X = 11 * 35
X = 11 * 35 / 11
X = 35

ie, Total number of students = 35

Students liking cricket = 2/5 * 35
= 14



2)
Let the number be X
So, 2 (X + 6) = 3X - 4
2X + 12 = 3X - 4
3X - 4 = 2X + 12
3X - 2X = 12 + 4
X = 16