Q. 25 A5.0( 2 Votes )

# A two–digit numbe

Let the two-digit number be xy(i.e. 10x + y).

After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).

According to question –

xy = 35…..(1)

And,

(10x + y) + 18 = (10y + x)

9x – 9y = – 18

x – y = – 2…..(2)

From equation(2), we get –

x = y – 2…..(3)

Substitute the value of x in equation(1), we get –

y(y – 2) = 35

y2 – 2y – 35 = 0

y2 – 7y + 5y – 35 = 0

y(y – 7) + 5(y – 7) = 0

(y – 7)(y + 5) = 0

y = 7 [ y = – 5 is invalid because digit of a number can't be – ve.]

Substituting the value of y in equation (3), we get –

x = 5

Thus, the required number is 57.

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