The sum of the two-digit number and the number obtained by interchanging the digits is 132. The digit in the ten’s place is 2 more than the digit in the unit’s place. Complete the activity to find the original number. Activity: Let the digit in the unit’s place is y and the digit in the ten’s place is 푥. ∴ The number = 10 푥 + 푦 ∴ The number obtained by interchanging the digits = ∴ The sum of the number and the number obtained by interchanging the digits = 132 ∴ 10 푥 + 푦 + 10 푦 + 푥 = ∴ x + y = (I) , By second condition, Digit in the ten’s place = digit in the unit’s place + 2 ∴ x – y = 2 . . . (II) Solving equation (I) and (II) ∴ x = y = Ans: The original number =
Answer:
The original number=75
Step-by-step explanation:
Let the unit digit=x
then digit at 10’s place=x+2
Then original number N =10*(x+2)+x
=10x+20+x
N=11x+20
Number formed after interchanging the digits
N’=10x+x+2=11x+2
Given that
N+N’=132
11x+20+11x+2=132
22x=132-22=110
x=110/22=5
Thus unit digit of original number=5
Digit at 10’s place=5+2=7
Thus the original number=75
Answer:
Original number =10x+y
=10(7)+5
=75