Question

A number consisting of two digits becomes 5/6 of itself, if it's digits are interchanged. If the difference of the digit is 1. Find the number. ​

Answer 1

let the two digit be x and y (x at ten's place and y at one's place)

so as per ques

x-y = 1

and the original number is 10x +y

so on interchaning the digits

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

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

=> 55y = 44x

since x-y = 1 => x = 1+y

so 55y = 44x

55y = 44(1+y)

55y = 44+44y

55y-44y = 44

=> y = 4 and x = 5

so original umber is

54

Hope it helps you.

Answer 2

Answer:

54

Step-by-step explanation:

 Let the required number be ab which can also be written as 10a + b. Here b is the unit digit and a is the tens digit.

 When, digits are reversed, new number ba or 10b + a.

According to question:

⇒ 5/6 of original no. = new no.

⇒ 5/6 or ( 10a + b ) = 10b + a

⇒ 5/6 * ( 10a + b ) = 10b + a

⇒ 5( 10a + b ) = 6( 10b + a )

⇒ 50a + 5b = 60b + 6a

⇒ 50a - 6a = 60b - 5b

⇒ 44a = 55b

⇒ 4a = 5b

       As given, difference between them is 1 ⇒ a - b = 1  ⇒ a = b + 1

⇒ 4( b + 1 ) = 5b

⇒ 4b + 4 = 4b

⇒ 4 = 5b - 4b = b

       hence, a = b + 1 = 4 + 1 = 5

Therefore the required number is ab or 54.