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A two digit no such that the sum of the digit is 12.when 1 is added to the no the digits interchange their places.find the nos.

2
by mchowdhary11

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by mchowdhary11

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There is a mistake in the given problem... It should be that, when 18 is added, the digits interchange their positions. If 1 is added then, the digits do not interchange places.

two digit number A B.

sum of the two digits = A + B = 12 --- (1)

The value of the number = 10 * A + B

Now 18 is added to the number: the value becomes : 10 A + B + 18

The number becomes: B A whose value = 10 B + A

Hence, 10 B + A = 10 A + B + 18

9 B = 9 A + 1

9 B = 9 (12 - B) + 1 -- by (1)

18 B = 108 + 18

B = 7

A = 5

*Given number is 57 , you add 18 , it becomes 75.*

two digit number A B.

sum of the two digits = A + B = 12 --- (1)

The value of the number = 10 * A + B

Now 18 is added to the number: the value becomes : 10 A + B + 18

The number becomes: B A whose value = 10 B + A

Hence, 10 B + A = 10 A + B + 18

9 B = 9 A + 1

9 B = 9 (12 - B) + 1 -- by (1)

18 B = 108 + 18

B = 7

A = 5