Question

the sum of the digits of two digit number is 9 if the digits are reversed the new number demonized by 9 equals 4 times of original number find the original number.
please give answer first

Answer 1

Let

Ten's place digit = x

units place digit = (9-x)

the original number = 10x + (9 - x )

=10x + 9 - x

=9x + 9 ------(1)

If digits are reversed the

new number = 10(9 - x ) + x

= 90 - 10x + x

= 90 - 9x ------(2)

relation given between (1) and (2) is

(2) - 9 = 4 × (1)

90 - 9x - 9 = 4 ( 9x + 9 )

81 - 9x = 36x + 36

divide each term with 9 we get

9 - x = 4x + 4

9 - 4 = 4x + x

5 = 5x

therefore

x = 1

put x=1 in (1)

Required number = 9x + 9

= 9 × 1 + 9

= 9 + 9

= 18

Hope this will helps you.

Answer 2

Answer:

let the numerator be x

so, the denomination is x+2

fraction formed = x/x+2

according to the question:

=>x/x+2+3=1/2

=> x/5 = 1/2

transposing 5 to rhs

=> x=5/2

hence, the rational no. is 5/2