Average of the marks of 132 students of a college is 40. If the average of the marks of the passed students is 42 and the average of the ma…

Average of marks of 132 students = Sum of marks of 132 students/132

⇒ 40 = Sum of marks of 132 students/132

⇒ Sum of marks of 132 students = 5280

Let number of passed student be x

Number of failed student = 132 – x

Now,

Average of marks of passed student = sum of marks of passed students/x

⇒ 42 = sum of marks of passed students /x

⇒ sum of marks of passed students = 42x

Now,

Average of marks of failed student = sum of marks of failed students/(132 – x)

⇒ 20 = sum of marks of failed students /(132 – x)

⇒ sum of marks of failed students = 20(132 – x) = 2640 – 20x

Now,

Total sum = 42x + 2640 – 20x

⇒ 5280 = 22x + 2640

⇒ 22x = 2640

⇒ x = 120

Total marks of passed student = 42x = 42 × 120 = 5040

⇒ Total marks of failed student = 2640 – 20x = 2640 – 20(120) = 240

∴ Required ratio = 5040 ? 240 = 21 ? 1