Question

Plz solve the 10 question​

Answer 1

Given :- The sum of the digits of a two - digit number is 9 . if the digits are interchanged , the number obtained exceeds the original number by 27 . Find the number ?

Solution :-

Let us assume that, the original two digit number is (10x + y) .

and, when digits are interchanged , number will be (10y + x) .

given that,

→ sum of digits = 9

So,

→ x + y = 9 ------------- Eqn.(1)

also,

→ Interchanged number - Original number = 27

→ (10y + x) - (10x + y) = 27

→ 10y - y + x - 10x = 27

→ 9y - 9x = 27

→ 9(y - x) = 27

→ y - x = 3 --------------- Eqn.(2)

Adding Eqn.(1) and Eqn.(2) , we get,

→ (x + y) + (y - x) = 9 + 3

→ x - x + y + y = 12

→ 2y = 12

→ y = 6 .

Putting value of y in Eqn.(1) ,

→ x + 6 = 9

→ x = 9 - 6

→ x = 3 .

Therefore,

→ Original Number = 10x + y = 10*3 + 6 = 30 + 6 = 36 (Ans.)

Hence, The number is 36 .

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