Question

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

Answer 1

$\large{\textbf{\underline{Smallest number is 9}}}$

$\huge{\textbf{\underline{As per Question:-}}}$

Let the three numbers be x , y and z.

$\huge{\textbf{\underline{Solution:-}}}$

• Second number is half the first.

$\textbf{ y = \dfrac{x}{2} }$

$\textbf{ x = 2y }$

• Third number is three times the first.

$z = 3x$

$z = 3 \times 2y$

$\textbf{ z = 6y }$

$\large{\textbf{\underline{Average of numbers is 27 }}}$

$\textbf{ 27 = \dfrac{x+y+z}{3} }$

$81 = x + y +z$

• put the value of x and z.

$81 = 2y + y + 6y$

$81 = 9y$

$y = \dfrac{81}{9}$

$y = 9$

$\large{\textbf{\underline{Required numbers are :-}}}$

y = 9

x = 2y = 2 × 9 = 18

z = 6y = 6 × 9 = 54

$\large{\textbf{\underline{Smallest number is 9}}}$

Answer 2

AnswEr :

Let the Numbers be a , b and c.

⋆ Given :

Second No. = Half of First No.

b = 1 / 2 × a

b = a / 2 —(¡)

Third No. = Three Times the First No.

c = 3 × a —(¡¡)

• According to Question Now :

⇒ Average of Numbers = 27

⇒ (a + b + c) / 3 = 27

⇒ (a + b + c) = 27 × 3

⇒ (a + b + c) = 81

• Putting the Values from (¡) & (¡¡)

⇒ (a + a / 2 + 3a) = 81

⇒ (2a + a + 6a) / 2 = 81

⇒ (2a + a + 6a) = 81 × 2

⇒ 9a = 162

⇒ a = 162 / 9

⇒ a = 18

• Using the Value of a in (¡) and (¡¡)

⇒ b = a / 2

⇒ b = 18 / 2

⇒ b = 9

⇒ c = 3 × a

⇒ c = 3 × 18

⇒ c = 54

჻ Required Numbers are 18, 9 and 54.