Question

The sum of the digits of a 2 digit number is 12. The given number exceeds the number obtained by interchanging the digits by 36. Find the given number

Answer 1

ans 84, sum 8+4=12 interchange 48
84-48=36

Answer 2

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☞ Number = 84

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$\huge\sf\blue{Given}$

✭ A number consists of 2 digits. The sum of its digits is 12

✭ The number obtained by interchanging the digits is 36 less than the given number

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◈ The Number?

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Case 1

Let the number be Number = 10x + y

$\leadsto\sf{x + y = 12...1)\qquad-eq(1)}$

Case 2

➢ Number obtained on reversing the digits = 10y + x

➢ Number obtained by reversing the digits = Original number - 36

$\sf{\dashrightarrow 10y + x = 10x + y - 36}$

$\sf{\dashrightarrow 36 = 10x + y -(10y + x)}$

$\sf{\dashrightarrow 36 = 10x + y - 10y - x }$

$\sf{\dashrightarrow 36 = 9x - 9y }$

On dividing both sides by 9

$\sf{\leadsto x - y = 4\qquad-eq(2)}$

$\sf{\leadsto x = 4 + y }$

Put the value of x from eq(2) in eq(1)

$\sf{\twoheadrightarrow (4+y) + y = 12}$

$\sf{\twoheadrightarrow 4 + 2y = 12 }$

$\sf{\twoheadrightarrow 2y = 12-4}$

$\sf{\twoheadrightarrow 2y = 8 }$

$\sf{\twoheadrightarrow y = \dfrac{8}{2}}$

$\sf{\orange{\twoheadrightarrow y = 4 }}$

Put the value of y in eq(2)

$\sf{\rightarrowtail x - 4 = 4 }$

$\sf{\rightarrowtail x = 4 + 4 }$

$\sf{\orange{\rightarrowtail x = 8}}$

Hence now,

➝ Number = 10x + y

➝ Number = 10(8) + 4

➝ Number = 80 + 4

➝ $\sf\red{Number = 84}$

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