the digits of a2-digit number different by 5.if the digits interchanged and the resulting number is added to the original number , we get 99.find the original number.
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Answered by
1
Answer:
Let the number be 10x + y
Given,
x-y=5
10x+y+10y+x=99
To find,
10x+y
Solution,
11x+11y=99
11(x+y)=99
x+y=9
x+y=9
x-y=5
2x=14
x=7
x-y=5
7-y=5
y=2
∴10x+y=70+2=72
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Answered by
2
Answer :-
Let the unit's digit be x
Ten's digit = 5 + x
Original number = 10 ( 5 + x ) + x
After interchanging the digits :-
→ Unit's digit = 5 + x
→ Ten's digit = x
Resulting number = 10x + 5 + x
According to the question :-
→ Resulting number + Original number = 99
→ 10x + 5 + x + 10 ( 5 + x ) + x = 99
→ 10x + 5 + x + 50 + 10x + x = 99
→ 10x + x + 10x + x + 50 + 5 = 99
→ 11x + 11x + 55 = 99
→ 22x + 55 = 99
→ 22x = 99 - 55
→ 22x = 44
→ x = 44 / 22
→ x = 2
- Unit's digit = x = 2
- Ten's digit = 5 + x = 5 + 2 = 7
Original number = 72
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