Question

The sum of the digits of a two digit number is 7. If
the digits are reversed, the new number decreased by
2, equals twice the original number. Find the number.
The ten's digit of a two digit number is three times
the unit digit. The sum of the number and the unit
digit is 32. Find the number.​

Answer 1

Let the units digit be x.

The tens digit =7−x.

Original no. =10(7−x)+x=70−9x

If digits are reversed, no. =10x+7−x=9x+7

9x+7−2=2(70−9x)

9x+5=140−18x

27x=135

x=5

Tens digit =7−5=2

Number =25

Let the two numbers be x and y. If x is the number in the 10th digit and y is the unit digit, then

x = 3y

and 10x+y+y = 32

10x + 2y = 32

and x = 3y. Substituting the value of x in 10x+2y = 32, we get

10 * 3y +2y = 32

or 32y = 32 or y = 1

and x = 3.

Thus, the number is 31.

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