The sum of the digits of a two digit number is 8. The digits of number get reversed when 18 is subtracted from the number. Find the original number.
32
62
53
71
A
32
B
62
C
53
D
71
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Solution
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Let x= the 10′s digit and y= be the unit digit
∴10x+y=original number
The sum of the digits of a two digit number is 8.
⇒x+y=8.....(1)
The digits of number get reversed when 18 is subtracted from the original number.
∴ Reversed digit = original number −18
⇒10y+x=10x+y−18
⇒10y−y=10x−x−18
⇒9y=9x−18
⇒y=x−2
Put the value of y in (1)
⇒x+x−2=8
⇒2x=8+2
⇒2x=10
⇒x=102=5
⇒x+y=8
⇒5+y=8
⇒y=8−5
⇒y=3
∴ Original number =53
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