Correct Option: A

let us assume the ten's digit number be x and unit's place digit be y.
Then two digit Original Number = 10x + y
According to question → y = 2x - 1 ................(1)
When digits are interchanged then new number = 10y + x
If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20,
New Number - Original Number = Original number - 20
⇒ 10y + x - (10x + y) = 10x + y - 20
⇒ 10y + x - 10x - y - 10x - y = - 20
⇒ 8y - 19x = - 20
⇒ 19x - 8y = 20 ...................(2)
Put the value of y from equation (1) in above equation (2).
⇒ 19x - 8(2x - 1) = 20
⇒ 19x - 16x - 8 = 20
⇒ 7x = 20 + 8
⇒ 7x = 28
⇒ x = 28/7
⇒ x = 4
Put the value of y in equation (1)
From (i) y = 2 x 4 -1 = y = 7
∴ original number = 10x + y =10 x 4 + 7 = 47.