In 2007, the arithmetic mean of the annual... | গাণিতিক যুক্তি Multiple Choice Question

Question: In 2007, the arithmetic mean of the annual incomes of Jarif and Naim was Tk 3800. The arithmetic mean of the annual incomes of Naim and Jamil was Tk 4800, and the arithmetic mean of the annual incomes of Jamil and Jarif was Tk 5800. What is the arithmetic mean of the incomes of the three?

Solution: It is given that in 2007, the arithmetic mean of the annual income of,
Jarif and Naim = 3800 Tk.
Naim and Jamil = 4800 Tk.
Jamil and Jarif = 5800 Tk.

Let a, b, and c be the annual incomes of Jarif, Naim, and Jamil, respectively.

Now, we are given that the arithmetic mean of the annual incomes of Jarif and Naim was Tk 3800.
Hence, (a + b)/2 = 3800
⇒ a + b = 2 × 3800 = 7600 -----------------------(1)

The arithmetic mean of the annual incomes of Naim and Jamil was Tk 4800.
Hence, (b + c)/2 = 4800
⇒ b + c = 2 × 4800 = 9600 -------------------------(2)
The arithmetic mean of the annual incomes of Jarif and Jamil was Tk 5800.
Hence, (c + a)/2 = 5800
⇒ c + a = 2 × 5800 = 11,600 -------------------------(3)

Summing these three equations(1+2+3) yields,
⇒ (a + b) + (b + c) + (c + a) = 7600 + 9600 + 11,600
⇒ 2a + 2b + 2c = 28,800
⇒ a + b + c = 14,400
The average of the incomes of the three equals the sum of the incomes divided by 3:
⇒ (a + b + c)/3 = 14,400/3 = 4800

In 2007, the arithmetic mean of the annual incomes of Jarif and Naim was Tk 3800. The arithmetic mean of the annual incomes of Naim and Jamil was Tk 4800, and the arithmetic mean of the annual incomes of Jamil and Jarif was Tk 5800. What is the arithmetic mean of the incomes of the three?

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