Question

The average age of All, Bilal and Changeez is 10 years. If the average age of Ali and Bilal be 12
years and that of Bilal and Changeez be 11 years, then the age of Bilal is:​

Answer 1

Answer:-

Given:

Average age of Ali , Bilal and Changeez is 10 years.

Let , Ali's age be x , Bilal's age be y and Changeez's be z years.

We know that,

Average/mean = Sum of observations/Number of observations.

Here,

• Sum of observations = x + y + z
• Number of observations (people) = 3

→ 10 = (x + y + z) / 3

→ 10*3 = x + y + z

→ x + y + z = 30 -- equation (1)

And,

Average age of Ali and Bilal is 12 years.

→ (x + y) / 2 = 12

→ x + y = 12 * 2

→ x + y = 24 -- equation (2)

Similarly,

→ (y + z) / 2 = 11

→ y + z = 2 * 11

→ y + z = 22 -- equation (3)

Now , Subtract equation (2) from (1).

→ x + y + z - (x + y) = 30 - 24

→ x + y + z - x - y = 6

→ z = 6

→ Changeez's age = 6 years

Substitute the value of z in equation (3).

→ y + z = 22

→ y + 6 = 22

→ y = 22 - 6

→ y = 16

Hence, the age of Bilal is 16 years.

Put the value of y in equation (2).

→ 16 + x = 24

→ x = 24 - 16

→ x = 8

→ Ali's age = 8 years.

Answer 2

Step-by-step explanation:

Assume that the age of Ali is x, Bilal is y and Changeez is z years.

As per given condition,

→ (x + y + z)/3 = 10

→ x + y + z = 30

→ z = 30 - x - y ..................(1)

Also,

→ (y + z)/2 = 11

→ y + z = 22

→ y + (30 - x - y) = 22 [From (1)]

→ y + 30 - x - y = 22

→ x = 8

Substitute value of x in (1)

→ z = 30 - 8 - y

→ z = 22 - y ...........(2)

Also said that, average age of Ali and Bilal be 12 years.

→ (x + y)/2 = 12

→ x + y = 24

→ y = 24 - 8

→ y = 16

Substitute value of y in (2)

→ z = 22 - 16

→ z = 6

Hence, the age of Bilal is 16 years.