The sum of the digits of a two digit number is 10. The number formed by interchanging the digits is 36 less than the original number. Find the original number.
NCERT CLASS VIII A
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The sum of the digits of a two digit number is 10. The number formed by interchanging the digits is 36 less than the original number. Find the original number.
NCERT CLASS VIII A
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Answer:
hi !!
Step-by-step explanation:
Let x = units digit
y = ten's digit
The value of the number is x + 10y
The new value after reversing the digits is 10x + y
Equations:
x + y = 10 and
10x + y = x + 10y - 36 or 9x - 9y = -36 or x - y = -4
Add the 2 equations, the result is 2x = 6
so x = 3 and y = 7
The original number is 73.
hope this helps u !!!
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Verified answer
Answer:
Let the unit's digit be x
Ten's digit = 10 - x
[tex]new \: number = 10 \times x + 10 - x = 10x + 10 - x = 9x + 10 \\ \\ number \: after \: interchanged \: = 10(10 - x) + x = 100 - 10x + x = 100 - 9x \\ \\ acq \\ \\ 9x + 10 = 100 - 9x - 36 \\ \\ 9x + 10 = 64 - 9x \\ \\ 9x + 9x = 64 -10 \\ \\ 18x = 54 \\ \\ x = 3 \\ \\ [/tex]
Unit's digit = 3
Ten's digit = 10 - 3 = 7
Number = 73