Question

The sum of the digits of a two-digit number is 10. The number formed by reversing the digits is 18 less
than the original number. Find the original number.


plzz solve this question with linear equations in one variable not to be solved with two variable..............

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Answer 1

Gɪᴠᴇɴ :-

The sum of the digits of a two-digit number is 10. The number formed by reversing the digits is 18 less than the original number.

ᴛᴏ ғɪɴᴅ :-

• Original number
• Reversed number

sᴏʟᴜᴛɪᴏɴ :-

Let the digit at tens place be x and ones place be y

then,

According to 1st condition :-

• Tens place digit + Ones place digit = 10

• x + y = 10. --(1)

According to 2nd condition :-

• Original number = (10x + y)
• Reversed number = (10y + x)

• Original no - 18 = Reversed no

➮ (10x + y) - 18 = (10y + x)

➮ 10x - x + y - 10y = 18

➮ 9x - 9y = 18

➮ 9(x - y) = 18

➮ x - y = 18/9

➮ x - y = 2. --(2)

On adding (1) and (2) , we get,

➮ (x + y) + (x - y) = 10 + 2

➮ 2x = 12

➮ x = 12/2

➮ x = 6

Put x = 6 in (1) , we get,

➮ x + y = 10

➮ 6 + y = 10

➮ y = 10 - 6

➮ y = 4

Hence,

• Tens place = x = 6
• Ones place = y = 4

Therefore,

• Original number (10x + y) = 64
• Reversed number (10y + x) = 46

Answer 2

$\bf{\underline{\underline \green{Solution:-}}}$

$\underline\mathtt \orange{AnswEr:}$

• $\small\pink{\underline {\boxed{\sf\pink{ The\: original\: number \: = 64} }}}$

$\underline\mathtt \orange{Given:}$

• The sum of the digits of a two-digit number is 10.
• The number formed by reversing the digits is 18 less than the original number.

$\underline\mathtt \orange{Need\:To\:Find:}$

• The original number = ?

$\bf{\underline{\underline \green{Explanation:-}}}$

$\mathsf {Let \:the \:two\: digit \:number\: be \:10x \:+ \:y}$

• $\mathsf {Where\: x \:>\: y}$

$\underline\mathtt \orange{Here:}$

$\longmapsto \sf {x + y = 10 ...(i)}$

$\underline\mathtt \orange{And:}$

$\longrightarrow \sf {10x + y - 10y - x = 18}$

$\longrightarrow \sf { 9x - 9y = 18}$

$\longrightarrow \sf { 9 (x - y) = 18}$

$\underline\mathtt \orange{Now,\:Here:}$

$\longmapsto \sf { x - y = 2 ...(ii)}$

$\underline\mathtt \orange{Solving \:equations \:(i) \:and\: (ii),}$

$\longmapsto \sf {x = 6 \:and\: y = 4}$

$\underline\mathtt \orange{Therefore:}$

$\mathsf{Original\: Number\: = \:10 \times 6 + 4}$

$\textbf {Original Number = 64}$

$\underline\mathtt \orange{Hence:}$

• $\small\pink{\underline {\boxed{\sf\pink{ The\: original\: number \: is \: 64.} }}}$

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