Question

the sum of a number of two digits and the number obtained on interchanging the digits is 99. if 5 is added to the number then it is 4 less than 6 times the sum of the digits. find the number​

Answer 1

Answer:

45

Step-by-step explanation:

Let the number be xy

10x+y+10y+x=99

11x+11y=99

/11

x+y=9.....................(1)

ii condition

10x+y+5 = 6(x+y)-4

10x+y+5=6x+6y-4

4x-5y=-9..................(2)

solve (1) &(2)

1 x + 1 y = 9 .............1

4 x -5 y = -9 .............2

-5 y

multiply (1)by 5

Multiply (2) by 1

5 x 5 y = 45

4 x -5 y = -9

Add the two equations

9 x = 36

/ 9

x = 4

plug value of x in (1)

1 x + 1 y = 9

4 + y = 9

y = 9 -4

y = 5

y = 5

the number is 45