Question

One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the sections will have equal number of students. If 4 times of students of section C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections

Answer 1

Let the number of students in section A be “x”

Let the number of students in section B be “y”

Let the number of students in section C be “z”

By the given first condition

x + y + z = 150  ...(1)

again by the second condition

x – 6 = z + 6

x – z = 6 + 6

x – z = 12  ...(2)

again by the third condition

x + y = 4z

x + y – 4z = 0

x + y – 4z = 0 ….(3)

Subtracting (1) and (3)

(1) ⇒ x + y + z = 150
(3) ⇒ x + y –  4z = 0
        (–)  (–)    (+)   (–)                
        0  + 0  + 5z = 150
                         z = `150/2` = 30

Substitute the value of z = 30 in (2)

x – 30 = 12

x = 12 + 30

= 42

Substitute the value of x = 42 and z = 30 in (1)

42 + y + 30 = 150

y + 72 = 150

y = 150 – 72

= 78

Number of students in section A, B and C are = 42, 78 and 30.