Math, asked by xMissGorgeousx, 7 months ago

Heya solve it and kindly flw bck​

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Answered by Anonymous
24

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★ Question :-

Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting number is greater than the original number by 63. Find the numbers .

★ Solution :-

Given,

» Sum of the digits = 9

» New number after interchanging the digits = Original number + 63

• Let the unit digit be 'x' and the tens place digit be 'y'. Then,

 \: \: ➠ \: \: \boxed{\rm{Original \: number \: = \bold{10y \: + \: x}}}

 \: \: ➠ \: \: \boxed{\rm{New \: number \: after \: changing \: digits \: = \: \bold{10x \: + \: y}}}

Now using the given things, we form equations as :-

~ Case I :-

➮ x + y = 9

➮ x = 9 - y ... (i)

~ Case II :-

➮ 10x + y = 10y + x + 62

➮ 10x + y - 10y - x = 62

➮ 9x - 9y = 62 ... (ii)

From equations (i) and equations (ii), we get,

➮ 9(9 - y) - 9y = 63

➮ 81 - 9y - 9y = 63

➮ -18y = 62 - 81

➮ -18y = -18

➮ 18y = 18

 \: \longrightarrow \: \: \huge{\bold{y \: = \: \dfrac{18}{18}}}

➮ y = 1

• So, tens place digit = y = 1

Now using equation (i) and value of y, we get,

➮ x = 9 - y

➮ x = 9 - 1

➮ x = 8

• So, unit place digit = x = 8

Then, using bot values of x and y, we get,

»Original number = 10y + x = 10(1) + 8 = 18

» New Number = 10x + y = 10(8) + 1 = 81

 \: \: \boxed{\sf{Hence \: the \: original \: number \: is \: \underline{18} \: and \: the \: new \: number \: after \: changing \: the \: digits \: is \: \underline{81}}}

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 \boxed{\tt{Confused ?, \: Don't \: worry \: let's \: verify \: it}}

For verification, we must simply apply the values we got into the equations we formed.

~Case I :-

:⟹ x + y = 9

:⟹ 8 + 1 = 9

:⟹ 9 = 9

Clearly, LHS = RHS

Here the condition satisfies, so our answer is correct.

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 \: \: \boxed{\tt{A \: piece \: of \: supplementary \: counsel}}

• Linear Equations in One Variable is the form of equations where we use to find the value of one variable using constant terms.

• Linear Equations are the form of linear polynomial with degree is equal to 1.

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