Question : The average of D1 and D2 is 40. The average of D2 and D3 is 45. The average of D1 and D3 is 55. What is the value of D3?
Option 1: 60
Option 2: 45
Option 3: 50
Option 4: 55
Correct Answer: 60
Solution :
Given: The average of D
1
and D
2
is 40.
The sum of D
1
and D
2
= 40 × 2 = 80 ---------------(1)
The average of D
2
and D
3
is 45.
The sum of D
2
and D
3
= 45 × 2 = 90 ----------------(2)
The average of D
1
and D
3
is 55.
The sum of D
1
and D
3
= 55 × 2 = 110 ------------(3)
Adding the equation (1), (2) and (3), we get,
D
1
+ D
2
+ D
2
+ D
3
+ D
1
+ D
3
= 80 + 90 + 110
⇒ 2 (D
1
+ D
2
+ D
3
) = 280
⇒ D
1
+ D
2
+ D
3
= 140
⇒ 80 + D
3
= 140
$\therefore$ D
3
= 60
Hence, the correct answer is 60.
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