Question

a number consists of two digits, the difference of whose digits is 5. if 8 times number is equal to the 3 times the number obtained by reversing the digits. find the number.​

Answer 1

Step-by-step explanation:

let number is xy, where x is ten's place and y is unit place

so it can be written as (10x + y)

given that |x - y| = 5

that is x - y = +5 ........eq(1)

or x-y = -5 .........eq(2)

Now,

8(10x + y) = 3(10y + x)

80x +8y = 30y +3x

77x -22y = 0

7x-2y = 0 ........eq (3

)

solving eq(1) and eq(3)

7x -2y = 0

-(2x-2y = 10)

it gives 5x = -10

x = -2

put in eq(1)

-2-y = 5

y =-7

so number => 10x + y = 10(-2) + (-7)

N=−27

solving eq(2) and eq(3)

7x-2y = 0

-(2x-2y = -10)

it gives , 5x = 10

x =2

put in eq(1)

2 - y = -5

y = 7

so, N = 10x + y = 10*2 + 7

N=27