Question

of the three numbers the second is half of the first and the third is three times the first.If average is 27 the smallest number is​

Answer 1

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=>Let the Numbers be $\bold{a,\:b\:and\:c}$

Given that :

Second No. = Half of First No.

b = 1 / 2 × a

b = a / 2 —(i)

Third No. = Three Times the First No.

c = 3 × a —(ii)

According to question:

⇒ Average of Numbers = 27

⇒ (a + b + c) / 3 = 27

⇒ (a + b + c) = 27 × 3

⇒ (a + b + c) = 81

Putting the Values from (i) & (ii)

⇒ (a + a / 2 + 3a) = 81

⇒ (2a + a + 6a) / 2 = 81

⇒ (2a + a + 6a) = 81 × 2

⇒ 9a = 162

⇒ a = 162 / 9

⇒ $\bold{a = 18}$

Using the Value of a in (i) and (ii)

⇒ b = a / 2

⇒ b = 18 / 2

⇒ $\bold{b = 9}$

⇒ c = 3 × a

⇒ c = 3 × 18

⇒ $\bold{c = 54}$

Therefore,

Required Numbers are :-

$\bold{18, 9 \:and \:54.}$