The sum of a two digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of its digits in the first number. Find the first number.
Answers
Given :
• The sum of a two digit number and the number formed by interchanging its digits is 110
• If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of its digits in the first number
To find :
• First number
Solution :
Let the two digit number be 10x + y where x and y are the digits.
The number formed by interchanging it's digits = 10y + x
According to the first condition given in the question,
→ 10x + y + 10y + x = 110
→ 11y + 11x = 110
→ 11(x + y) = 110
→ x + y = 10 ----(1)
According to the second condition given in the question,
→ (10x + y) - 10 = 4 + 5(x + y)
→ (10x + y) - 10 = 4 + 5x + 5y
→ 10x + y - 10 = 4 + 5x + 5y
→ 10x - 5x + y - 5y = 4 + 10
→ 5x - 4y = 14 -----(2)
→ Multiplying (1) by 4 :-
→ (x + y = 10) × 4
→ 4x + 4y = 40 ------(3)
Solving (3) and (4) :-
→ 4x + 4y = 40
→ 5x - 4y = 14
_____________
→ 9x = 54
_____________
→ 9x = 54
→ x = 6
Substitute the value of x in equation (1) :-
→ x + y = 10
→ 6 + y = 10
→ y = 10 - 6
→ y = 4
Therefore, the value of x = 6 and y = 4
Hence, the original two digit number is :-
→ 10x + y
→ 10(6) + 4
→ 64
Answer →
- The first number = 6