Question

The average of 5 number is 496 if 2 of then are 117 and 140 find the average of remaining three number

Answer 1

Given: The average of 5 number is 496. If 2 of them are 117 and 140.

Need to find: The average of remaining three numbers.

❒ Let the five numbers be $\sf x_{1}, x_{2}, x_{3}, x_4 \;and\; x_5.$

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$\underline{\bf{\dag} \:\mathfrak{As\; we \; know \; that \; :}}$

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$\star\;\boxed{\sf{\pink{Average = \dfrac{ Sum\; of\; observation}{Total \; number \; of \; observation}}}}$

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Also,

• The average of 5 number is 496.

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Therefore,

$:\implies\sf 496 = \dfrac{ x_1 + x_2 + x_3 + x_4 + x_5}{5} \\\\\\:\implies\sf Numbers = 496 \times 5 \\\\\\:\implies{\underline{\boxed{\frak{\purple{ 2480}}}}}\;\bigstar$

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \; the\; Question \: :}}}}\mid}$

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• The average of 5 number is 496. And, If two of them are 117 and 140.

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Therefore,

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• $\sf x_1$ = 117
• $\sf x_2$ = 140

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Now,

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$:\implies\sf 117 + 140 + x_3 + x_4 + x_5 = 2480 \\\\\\:\implies\sf x_3 + x_4 + x_5 = 2480 - 257 \\\\\\:\implies{\underline{\boxed{\frak{\pink{ x_3 + x_4 + x_5 = 2223}}}}}\;\bigstar$

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• By using same formula, finding the average of remaining three numbers.

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Hence,

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$:\implies\sf \dfrac{x_3 + x_4 + x_5}{3} \\\\\\:\implies\sf \cancel\dfrac{ 2223}{3} \\\\\\:\implies{\underline{\boxed{\frak{\purple{741}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence, \: the\; average\; of \: remaining \; three \; numbers \;is \; \bf{741}.}}}$

Answer 2

$\LARGE\mathfrak{\underline{\underline{ Given :-}}}$

$\large: \: \mapsto\texttt{Average of 5 numbers = 496}\\\\\large: \: \mapsto\texttt{2 numbers of them = 117 , 140}$

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$\LARGE\mathfrak{\underline{\underline{ To \: \: \: find :-}}}$

$\large\qquad{: \: \mapsto\texttt{Average of the remaining numbers}}$

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$\LARGE\mathfrak{\underline{\underline{Formula :-}}}$

$\large\qquad{: \: \Longrightarrow\underline{\boxed{\textsf{\textcolor{red}{Average = \cfrac{Sum \: \: \: of \: \: \: observation}{Total \: \: \: number\: \: \: of\: \: \: observations} }}}}}$

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$\LARGE\mathfrak{\underline{\underline{How \: \: \: To \: \: \: Solve:-}}}$

• Let's assume the numbers as a₁ , a₂ , a₃ , a₄ , a₅ .

• As we have been provided with the average of the 5 numbers that is 496 .

• So by this information we can calculate the total sum of all the digits .

• Also we have been provided with 2 numbers that are 117 , 140 . So we assum this two numbers as a₁ and a₂ .

• So , we add this numbers together and subtract it from the sum of the Total number.

• And from this final result we calculate the Average of the 3 numbers .

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$\LARGE\mathfrak{\underline{\underline{Solution :-}}}$

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• First we calculate the sum of all the five numbers with the help of the Formula.

$\large\: \bigstar\textsf\textcolor{orange}{\: \: \: Average = \cfrac{Sum \: \: \: of \: \: \: observation}{Total \: \: \: number \: \: \: of \: \: \: observations} }\\\\\\\large: \: \Longrightarrow\textsf{496 = \cfrac{a_{1} + a_{2} + a_{3} + a_{4} + a_{5}}{5} }\\\\\\\large: \: \Longrightarrow\textsf{Sum of no. = 496 × 5}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{purple}{Sum of no. = 2480 }}}$

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• We have successfully calculate the sum of all the digits.
• So now we have to subtract the sum of 2 numbers 117 , 140 from the total sum of all the numbers.

• We assume the two numbers as

1. a₁ = 117
2. a₂ = 140

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$\large\qquad{: \: \mapsto\texttt{ 117 + 140 + a_{3} + a_{4} + a_{5}= 2480 }}\\\\\large\qquad{: \: \mapsto\texttt{ 257 + a_{3} + a_{4} + a{5}= 2480 }}\\\\\large\qquad{: \: \mapsto\texttt{ a_{3} + a_{4} + a_{5}= 2480 - 257 }}\\\\\large\qquad{: \:\Longrightarrow\underline{\boxed{\textsf\textcolor{purple}{ a_{3} + a_{4} + a_{5}= 2223 }}}}$

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• So now we have also successfully calculated the sum of the 3 numbers.
• So now we have to calculate their average , by using the formula.

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$\large\: \bigstar\textsf\textcolor{orange}{\: \: \: Average = \cfrac{Sum \: \: \: of \: \: \: observation}{Total \: \: \: number\: \: \: of \: \: \: observations} }\\\\\\\large: \: \Longrightarrow\textsf{= \cancel\cfrac{2223}{3} }\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{purple}{Average = 741}}}$

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