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Three numbers are given in which the second is triple the first and is also double the third. If the average of the three numbers is 66, find the first number?
- A36
- B54
- C108
- D72
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CCommunity
Let the numbers be x, y and z
As per the given data,
y = 3x
x = y/3
⇒ y = 2z
⇒ z = y/2
Given that average of the three numbers is 66
⇒ (x + y + z)/3 = 66
⇒ (y/3 + y + y/2)/3 = 66
⇒ (2y + 6 y + 3y)/(3 × 6) = 66
⇒ 11y = 66 × 18
⇒ y = 108
∴ First number x = y/3 = 108/3 = 36
As per the given data,
y = 3x
x = y/3
⇒ y = 2z
⇒ z = y/2
Given that average of the three numbers is 66
⇒ (x + y + z)/3 = 66
⇒ (y/3 + y + y/2)/3 = 66
⇒ (2y + 6 y + 3y)/(3 × 6) = 66
⇒ 11y = 66 × 18
⇒ y = 108
∴ First number x = y/3 = 108/3 = 36