In a two-digit number, the digit at the unit's place is 1 less than twice the digit at the ten's place. 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. The original number is

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.