Question

The average age of A and B is 36 years, the average age of B and C is 35 years, and the average age of A and C is 29 years. what will be the age of A.

Answer 1

A+B=36*2=72

B+C=35*2=70

A+C=29*2=58

2(A+B+C)=200

A+B+C=100

A+70=100 Bcz B+C=70

A=100-70

A=30 years

Answer 2

The age of A is 30 years

Given :

• The average age of A and B is 36 years

• The average age of B and C is 35 years

• The average age of A and C is 29 years

To find :

The age of A

Solution :

Step 1 of 2 :

Form the system of equations

Let age of A , B , C are x years , y years and z years respectively

The average age of A and B is 36 years

∴ Sum of ages of A and B = 2 × 36 = 72 years

∴ x + y = 72 - - - - - (1)

The average age of B and C is 35 years

∴ Sum of ages of B and C = 2 × 35 = 70 years

∴ y + z = 70 - - - - - (2)

The average age of A and C is 29 years

∴ Sum of ages of A and C = 2 × 29 = 58 years

∴ x + z = 58 - - - - - (3)

Step 2 of 2 :

Calculate age of A

Adding Equation 1 and Equation 3 we get

2x + y + z = 130 - - - - (4)

Equation 4 - Equation 2 gives

2x = 60

⇒ x = 60/2

⇒ x = 30

Hence age of A is 30 years

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