The digit of two-digit number differ by 3. If digits are interchanged, and the resulting number is added to the original number, we get 121. Find the original number.
Answers
Answer:
The original number is 74.
Step-by-step-explanation:
Let the greater digit at tens place be x.
And the smaller digit at units place be y.
∴ Two-digit number = xy
⇒ Original number = 10x + y
From the first condition,
The digits of the original number differ by 3.
∴ x - y = 3
⇒ x = 3 + y
⇒ x = y + 3 - - - ( 1 )
Now,
The number obtained by interchanging digits = yx
⇒ New number = 10y + x
From the second condition,
Original number + New number = 121
⇒ 10x + y + 10y + x = 121
⇒ 10x + x + y + 10y = 121
⇒ 11x + 11y = 121
⇒ x + y = 11 - - - [ Dividing each term by 11 ]
⇒ ( y + 3 ) + y = 11 - - - [ From ( 1 ) ]
⇒ y + 3 + y = 11
⇒ y + y = 11 - 3
⇒ 2y = 8
⇒ y = 8 ÷ 2
⇒ y = 4
By substituting y = 2 in equation ( 1 ), we get,
x = y + 3 - - - ( 1 )
⇒ x = 4 + 3
⇒ x = 7
Now,
Original number = 10x + y
⇒ Original number = 10 * 7 + 4
⇒ Original number = 70 + 4
⇒ Original number = 74
∴ The original number is 74.