Question

The sum of the digits of a two-digit number is 10. If the digits are reversed, then the new number is 36 more than the original number. Identify the two-digit number​

Answer 1

Answer :

[ Given ]

The sum of two digit = 10

Then suppose first digit = x

And second digit = y

Then the equation found x + y = 10

Now interchanging the number is decreased by 36

(10x + y) = (10y - x) -36

Then 10x - x + y - 10y = -36

9x - 9y = -36

Then all are divided by 9

So second equation found => x - y = -4

Add first and second equation

x + y = 10

+ x - y = 4

=> 2x = 6

then x = 3

Now First equation = 3 + y = 10

y = 10-3 = 7

y =7

Then original number = (10x + y)

10 x 3 + 7

=> 37 Answer √√

Answer 2

• Let one's digit number be M and tens digit number be N.

Original number = 10N + M

》 The sum of two digits of a two digit number is 10.

=> M + N = 10

=> M = 10 - N __________ (eq 1)

》 If the digits are reversed, then the new number is 36 more than the original number.

Revered number = 10M + N

According to question,

=> 10M + N = 10N + M + 36

=> 10M - M + N - 10N = 36

=> 9M - 9N = 36

=> M - N = 4

=> 10 - N - N = 4 [From (eq 1)]

=> - 2N = - 6

=> N = 3 (ten's digit)

Put value of N in (eq 1)

=> M = 10 - 3

=> M = 7 (one's digit)

Number = 10N + M

=> 10(3) + 7

=> 30 + 7

=> 37

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Number = 37

_______________ [ ANSWER ]

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☆ VERIFICATION :

From above calculations we have M = 7 and N = 3

Put value of M and N in this : M + N = 10

=> 7 + 3 = 10

=> 10 = 10

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