sum of the digits of a two-digit number is 9. When we interchange the digits it found that the resulting new number is greater than the original number by 27 what is the two-digit number?
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Answers
Step-by-step explanation:
The new number is greater than the old number by 27, i.e. Adding the two equations, we get 2y = 12 or y = 6. Thus, x = 3. Therefore, the original number is 36.
Given :- sum of the digits of a two-digit number is 9. When we interchange the digits it found that the resulting new number is greater than the original number by 27 what is the two-digit number ?
Solution :-
Let us assume that, the given two digit number is 10x + y .
A/q,
→ x + y = 9 ------- Eqn.(1)
and,
difference between reverse = 27
→ (10y + x) - (10x + y) = 27
→ 9y - 9x = 27
→ 9(y - x) = 27
→ y - x = 3 --------- Eqn.(2)
adding Eqn.(1) and Eqn.(2),
→ x + y + y - x = 9 + 3
→ 2y = 12
→ y = 6
putting value of y in Eqn.(1),
→ x + 6 = 9
→ x = 9 - 6 = 3
therefore,
→ Required number = (10x + y) = 10*3 + 6 = 30 + 6 = 36 (Ans.)
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