Question

69. The sum of the digits of a two-digit number is 1/5 of the difference between the number and the number cbtained by interchanging the positions of the digits. What is definitely the difference between the digits of that number?
(a) 5
(b) 7
(c) 9
(d) Data inadequate
(e) None of these​

Answer 1

Answer:

☞ Option C

According to the question :

Let the ten's digit be ' x ' and unit / ones digit be ' y '

• One's = x , Ten's place = 10y
• Sum of digits = x + y
• Difference = 1 / 5
• Interchanging digits = ( x + y = y + x )

Equation :

x + y = 1 / 5 [ ( 10x + y ) - ( 10y + x ) ]

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

=> 5 ( x + y ) = 9x - 9y

=> 5x + 5y = 9x - 9y

=> 5y + 9y = 9x - 4x

=> 14y = 4x

=> x / y = 14 / 4

= > x / y = 7 / 2

To find :

x / y = 7 / 2

=> x = 7 and y = 2

=> x + y = 7 + 2

=> 9

♥ So, It's Done ♥ !!