Question

The result of dividing a number of two digits by the number with the digits reversed is 5/6.If the difference of digits is 1, find the number. problem from simultaneous linear equation.​

Answer 1

The solution of your problem is :-

Let the ten's digit be x and one's digit be y.

•°• The original number = 10x+y

and the reversed number = 10y+x

ATP:-

(10x+y)/(10y+x) = 5/6

=> 6(10x+y) = 5(10y+x)

=> 60x+6y = 50y+5x

=> 55x-44y = 0

=> 11(5x-4y) = 0 (taking 11 as common)

=> 5x-4y = 0/11 = 0.......(1)

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

multiply eq(2) by 5, we get

5(x-y) = 1×5

=>5x-5y = 5.......(3)

subtracting eq(1) & eq(3), we get

(5x-5y)-(5x-4y) = 5-0

=> 5x-5y-5x+4y = 5

=> -y = 5

=> y = -5

now putting the value of y in eq(2), we get

x-(-5) = 1

=> x+5 = 1

=> x = 1-5

=> x = -4

•°• the number is 10(-4)+(-5)

= -40-5 = -45 [Answer]

hope it helps.

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