Plz solve the 10 question
Answers
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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