Question

A two digit no is 3 more than 4 times the sum of its digits .If 18 is added to this no ,the sum is equal to the number obtained by interchanging the digits . find the number ( linear equation in two variable )

Answer 1

10x+y=3+4×(x+y)

10x+y=3+4x+4y

6x-3y=3

2x-y=1

10x+y+18=10y+x

9x-9y=-18

x-y=-2

-(2x-y=1)

-x=-3

x=3

6-y=1

-y=-5

y=5

no.==53

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Answer 2

Let the digits be x and y.

Thus, number=10x+y

Now,

(10x+y) - 4(x+y)= 3.....(i)

and

(10x+y)+ 18=10y+x.....(ii)

Solving (i)

10x+y-4x-4y=3

or,6x-3y=3

or,2x-y=1....(1)

Solving (ii)

10x+y-10y-x=-18

or, 9y-9x=18

or,y-x=2...(2)

(1)+(2)

2x-y+y-x=1+2

or,x=3

Thus, y=x+2 (from (2))

y=5

Therefore the number= 10x+y=10x3+5=35

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