Question

The average of three numbers is 30. The first is twice of second and second is one-third of third number. Find the numbers.​

Answer 1

•AnswEr :-

•Refer to the attachment.

Answer 2

Answer -

• The numbers are 45, 15 and 30 respectively.

To find -

• The numbers.

Step-by-step explanation :-

Let the third number be "x".

• As the second number is one-third of the third number,

Therefore,

• $\rm The \: second \: number \: will \: be \: \dfrac{1}{3} x$

Now, given that -

• The first number is twice of the second number.

Therefore,

• $\rm The \: first \: number \: will \: be \: 2 \times \dfrac{1}{3} x$

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• The average of the three numbers is 30.

We know that -

$\underline{ \boxed{ \sf Average = \dfrac{Sum \: of \: the \: Numbers}{Total \: Numbers} }}$

Here,

• Average = 30.
• Total numbers = 3.

Substituting the given values in this formula,

$\implies \bf\dfrac{x + \frac{1}{3}x + 2 \times \frac{1}{3}x }{3} = 30$

$\implies\bf \dfrac{x + \frac{x}{3} + 2 \times \frac{x}{3} }{3} = 30$

$\implies\bf \dfrac{x + \frac{x}{3} + \frac{2x}{3} }{3} = 30$

$\implies\bf x + \dfrac{x}{3} + \dfrac{2x}{3} = 30 \times 3$

$\implies\bf x + \dfrac{x}{3} + \dfrac{2x}{3} = 90$

$\implies \bf\dfrac{(x \times 3) + (x \times 1) + (2x \times 1)}{3} = 90$

$\implies\bf\dfrac{3x + x + 2x}{3} = 90$

$\implies\bf\dfrac{6x}{3} = 90$

$\implies\bf6x = 90 \times 3$

$\implies\bf6x = 270$

$\implies\bf x = \cancel{\dfrac{270}{6} }$

$\implies\bf x = 45$

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Hence, the numbers are :-

$\mapsto\tt x = 45.$

$\mapsto\tt \dfrac{1}{3} x = \dfrac{1}{3} \times 45 = \cancel{\dfrac{45}{3}} = 15.$

$\mapsto\tt2 \times \dfrac{1}{3} x = 2 \times \dfrac{1}{3} \times 45 = \cancel{\dfrac{90}{3}} = 30.$