Question

The sum of a two digit number and a number formed by interchanging its digit is 110 .If 10is subtracted from the original number,the new number is 4 more than 5 times the sum of digits of the original number.Find the original number

Answer 1

the original no is 610

Answer 2

let the digits be x and y
the number becomes 10x+y
on reversing the digits,the number becomes 10y+x
ATQ,
10X+Y+10Y+X= 110
11X+11Y=110
TAKING 11 COMMON
11(X+Y) =110
X+Y=110/11
X+Y=10---------(1)
X=10-Y
CASE 2
SUBTRACTING 10 FROM ORIGINAL NUMBER
10X+Y-10
5times the sum of digits of original number =5(X+Y)
ATQ,
10X+Y-10= 5(X+Y)+4
10X+Y-10=5(10)+4
10X+Y= 50+4+10
10(10-Y)+Y=64
100-10Y+Y=64
-9Y=64-100
-9Y= - 36
Y=4


PUTTING VALUE OF Y IN EQ 1
X+4=10
X=6

THEREFORE THE NUMBER BECOMES
10(6)+4=60+4=64

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