The average monthly income of Rakib and Sunny is Tk. 5050. The average monthly income of Sunny and Rabbi is Tk. 6250 and the average monthly income of Rakib and Rabbi is Tk. 5200. What is the monthly income of Rakib?

Question: The average monthly income of Rakib and Sunny is Tk. 5050. The average monthly income of Sunny and Rabbi is Tk. 6250 and the average monthly income of Rakib and Rabbi is Tk. 5200. What is the monthly income of Rakib?

Solution:
Rakib + Sunny (total income) = 5050 × 2 = 10100 .............. (i)
Sunny + Rabbi (total income) = 6250 × 2 = 12500 .............. (ii)
Rakib + Rabbi (total income) = 5200 × 2 = 10400 ................. (iii)

Adding (i), (ii) and (iii), we get:
2(Rakib + Sunny + Rabbi) = 10100 + 12500 + 10400
⇒ 2(Rakib + Sunny + Rabbi) = 33000
⇒ Rakib + Sunny + Rabbi = 16500 ........... (iv)

Subtracting (ii) from (iv), we get
Rakib = 16500 - 12500
∴ Rakib = 4000

∴ Rakib's monthly income = Tk. 4000.