Question

in 2 digit number once digit is 1 more than tens digit if we interchange the digits ratio of original and new number is 5:6 find original number​

Answer 1

Let the number in Tens digit be 'y'

And ones digit be 'x'.

Then the original number will be '10y +x.

Case 1

Ones digit is 1 more than the tens digit

∴ x = y + 1

→ x - y = 1 ..[1]

Case 2

( On interchanging the digits, the number will be 10x + y)

The ratio of the original and the number after interchanging the digits is 5 : 6

$\therefore\quad\rm \dfrac{10y+x}{10x+y}=\dfrac{5}{6}$

$\implies\rm 6(10y+x) = 5(10x+y)$

$\implies\rm 60y+6x = 50x+5y$

$\implies\rm 60y-5y= 50x-6x$

$\implies\rm 55y= 44x$

$\implies\rm 5y= 4x \quad \qquad ...[2]$

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Now, we have our equations as,

$\rm x - y = 1 \qquad ...[1]$

$\rm 5y = 4x \qquad ...[2]$

Multiplying [1] by 4 will give,

$\rm 4(x-y=1) \implies 4x-4y=4$

Since 5y = 4x , therefore

→ 4x - 4y = 4

→ 5y - 4y = 4

→ y = 4

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Substituting the value of y in [1]

→ x - y = 1

→ x - 4 = 1

→ x = 4 + 1

→ x = 5

______________

Original number = 10y + x

Substituting the values,

→ 10(4) + 5

→ 40 + 5

→ 45

Hence, the original number is 45.