the sum of the digitsof a 2 digits number is 12 of the new number reversing the digits greater than the original number 18 . find the original number.
Answers
Answer:
The original number is 57.
Step-by-step-explanation:
Let the digit at tens place be x.
And the digit at the units place be y.
∴ Original number = xy
∴ Original number = 10x + y
The number obtained by reversing the digits = yx
∴ The number obtained by reversing the digits = 10y + x
Now,
From the first condition,
Sum of digits is 12.
∴ x + y = 12
⇒ x = 12 - y - - - ( 1 )
From the second condition,
Number obtained by reversing digits = Original number + 18
∴ 10y + x = 10x + y + 18
⇒ 10y + x - 10x - y = 18
⇒ 10y - y - 10x + x = 18
⇒ 9y - 9x = 18
⇒ 9y - 9 ( 12 - y ) = 18 - - - [ From ( 1 ) ]
⇒ 9y - 108 + 9y = 18
⇒ 9y + 9y = 18 + 108
⇒ 18y = 126
⇒ y = 126 ÷ 18
⇒ y = 7
Now, by substituting y = 8 in equation ( 1 ), we get,
x = 12 - y - - - ( 1 )
⇒ x = 12 - y
⇒ x = 12 - 7
⇒ x = 5
Now,
Original number = 10x + y
⇒ Original number = 10 × 5 + 7
⇒ Original number = 50 + 7
⇒ Original number = 57
∴ The original number is 57.
─────────────────────
Verification:
The original number = 57
∴ The number obtained by reversing the digits = 75
From the condition,
75 = 57 + 18
⇒ 75 = 75
∴ LHS = RHS
Hence verified!
Answer:
The original number is 57.
Step-by-step-explanation:
Let the digit at tens place be x.
And the digit at the units place be y.
∴ Original number = xy
∴ Original number = 10x + y
The number obtained by reversing the digits = yx
∴ The number obtained by reversing the digits = 10y + x
Now,
From the first condition,
Sum of digits is 12.
∴ x + y = 12
⇒ x = 12 - y - - - ( 1 )
From the second condition,
Number obtained by reversing digits = Original number + 18
∴ 10y + x = 10x + y + 18
⇒ 10y + x - 10x - y = 18
⇒ 10y - y - 10x + x = 18
⇒ 9y - 9x = 18
⇒ 9y - 9 ( 12 - y ) = 18 - - - [ From ( 1 ) ]
⇒ 9y - 108 + 9y = 18
⇒ 9y + 9y = 18 + 108
⇒ 18y = 126
⇒ y = 126 ÷ 18
⇒ y = 7
Now, by substituting y = 8 in equation ( 1 ), we get,
x = 12 - y - - - ( 1 )
⇒ x = 12 - y
⇒ x = 12 - 7
⇒ x = 5
Now,
Original number = 10x + y
⇒ Original number = 10 × 5 + 7
⇒ Original number = 50 + 7
⇒ Original number = 57
∴ The original number is 57.
─────────────────────
Verification:
The original number = 57
∴ The number obtained by reversing the digits = 75
From the condition,
75 = 57 + 18
⇒ 75 = 75
∴ LHS = RHS
Hence verified!