Question

the sum of the digits of a 2 digit no is 15 the no is decresed by 27 if the digits are reversed find the no

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Answer 1

Step-by-step explanation:

given sum of digit

x + y = 15 ----1

when it is decresed by 27

10x+y - 27 = 10y+x

9x - 9y = 27

×-y = 3

therefore solving both eq .

x = 9 y = 6

required no.

96

Answer 2

Answer :-

96

Solution :-

Let the units place be y and tens place be x

Sum of digits = 15

==> x + y = 15

==> y = 15 - x -- (Equation 1)

We Know that

General form of 2 digit no. :-

10 × Tens place + Units place

Number formed i.e Original number = 10x + y

Number obtained when digits are reversed = 10y + x

Given :-

Original no. - 27 = Reversed no.

==> 10x + y - 27 = 10y + x

==> 10x - x + y - 10y = 27

==> 9x - 9y = 27

==> x - y = 3

From Equation 1

==> x - (15 - x) = 3

==> x - 15 + x = 3

==> 2x - 15 = 3

==> 2x = 3 + 15

==> 2x = 18

==> x = 18/2

==> x = 9

Substituting x = 9 in Equation 1

==> y = 15 - x

==> y = 15 - 9 = 6

Original no. = 10x + y = 10 × 9 + 6 = 90 + 6 = 96

Therefore the required number is 96.