Question

the sum of the digits of a two-digit number is 8. if its digits are reverse, the new number so formed is decreased by 18 . the number is
(a) 37
(b) 48
(c) 53
(d) 46

Answer 1

Let ones digit be x
ten's digit be. y

Original no = 10(Ten's digit)+ones digit
= 10(y)+x
= 10y+x


(x+y=8, x=8-y)


By Condition


One's digit = y
Ten's digit= x


New No. = 10x+y


According to the question


10x+y=10y+x-18

10x-x =10y-y-18

9x. = 9y-18

9(x). = 9(y-2)

x. = y-2

Put the value of x


8-y. = y-2

8+2= y+y
10. =2y

y. = 10/2=5


x=8-y
x=8-5=3


Original no. = 10(Ten's digit) + Ones digit

= 10(y)+x
= 10(5)+3 =50+3=53