Question

a two digit number is such that the tens digit of the number exceeds twice the units digit by 5 and the number obtained interchanging the digits is 7 more than twice the digits find the number

Answer 1

Answer: Let xy be the required two-digit number.

Let x be the number which is in unit's digit.

Let y be the number which is in ten's digit.

Therefore the decimal expansion is 10x+y.    ------- (1)

Given that the 10's digit exceeds twice the unit digit by 2.

x = 2y + 2.   ------- (2).

Also, Given that the number obtained by interchanging the digits is 5 more than the sum of the digits.

10y + x = 3(x + y) + 5

10y + x = 3x + 3y + 5

10y + x - 3x - 3y = 5

7y - 2x = 5

7y - 2(2y + 2) = 5 (from (2))

7y - 4y - 4 = 5

3y - 4 = 5

3y = 9

y = 3   ------ (3)

Substitute (3) in (2), we get

x = 2(3) + 2

x = 6 + 2

x = 8.    ----- (4)

On substituting (3) & (4) in (1), we get

The number is 10x + y = 10 * 8 + 3

                                    = 80 + 3

                                    = 83.

Therefore, the required two-digit number is 83.

Hope this helps!

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