Question

a two numbers become 5/6 th of itself when it's reversed .the two digits differ by the number is ​

Answer 1

Answer:

Let the number be =10a+b

10b+a=65(10a+b),anda−1=b,5(10a+a−1)=6(10a−10+a)55a−5=66a−60,11a=55,a=5,b=4

Answer 2

""" ❤️ Answer ❤️ """

Let the digit at ten's place be x and the digit at unit's place be y

Difference between digits = 1

⇒ x - y = 1

⇒ x - 1 = y

Number formed by the digits = 10x + y

Number obtained when digits are reversed = 10y + x

Given :

Number becomes 5/6th itself when digits are reversed

\implies \dfrac{5}{6} (10x + y) = 10y + x

⇒ 5(10x + y) = 6(10y + x)

⇒ 50x + 5y = 60y + 6x

⇒ 50x - 6x = 60y - 5y

⇒ 44x = 55y

⇒ 4x = 5y

Substituting y = x - 1

⇒ 4x = 5(x - 1)

⇒ 4x = 5x - 5

⇒ 5 = 5x - 4x

⇒ 5 = x

⇒ x = 5

Substituting x = 5 in y = x - 1

⇒ y = 5 - 1 = 4

Number = 10x + y = 10(5) + 4 = 50 + 4 = 54

Hence, the number is 54 .