The average per day income of A, B and C is Rs. 45. If the average per day income of A and B is Rs. 40 and that of B and C is Rs. 43, then the per day income of B is :

Given:

The average per day income of A, B, and C = Rs. 45

The average per day income of A and B = Rs. 40

The average per day income of B and C = Rs. 43

Formula Used:

Average = (Sum of incomes) / (Number of people)

Calculation:

Let the per day incomes of A, B, and C be a, b, and c respectively.

From the given data:

\(\frac{a + b + c}{3} = 45\)

⇒ a + b + c = 45 × 3

⇒ a + b + c = 135

\(\frac{a + b}{2} = 40\)

⇒ a + b = 40 × 2

⇒ a + b = 80

\(\frac{b + c}{2} = 43\)

⇒ b + c = 43 × 2

⇒ b + c = 86

We have the following equations:

1) a + b + c = 135

2) a + b = 80

3) b + c = 86

Subtract equation 2 from equation 1:

⇒ c = 135 - 80

⇒ c = 55

Subtract equation 3 from equation 1:

⇒ a = 135 - 86

⇒ a = 49

Now, using equation 2:

⇒ b = 80 - a

⇒ b = 80 - 49

⇒ b = 31

The per day income of B is Rs. 31.