Question

In a two digit number the ten's digit is twice unit's digit. If 27 is added to the number the digits interchange their places. Find the number

Answer 1

Answer:

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Answer 2

☯ Let the digit in the unit's place be x and digit in the ten's place be y.

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Therefore,

Number = 10y + x

And,

Number obtained by reversing the digit = 10x + y

★ According to Question:

The ten's digit is twice unit's digit

➠ x = 2y⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀....eq (1)

If 27 is added to the number the digits interchange their places.

Number + 27 = Number obtained by interchanging the digits

Therefore,

➠ 10y + x + 27 = 10x + y

➠ 9x - 9y = 27

➠ 9(x - y) = 27

➠ x - y = 27/9

➠ x - y = 3⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀....eq (2)

☯ Now, Putting value of x from eq (1) into eq (2),

➠ 2y - y = 3

➠ y = 3

☯ Putting vale of y in eq (2),

➠ x - 3 = 3

➠ x = 3 + 3

➠ x = 6

∴ Hence, The number is 10y + x = 10 × 3 + 6 = 36.