The sum of the digits of a 2 digits number is 9 .The number is 6times the units digit find the number
Answers
Given :
• Sum of the digits of a 2 digit number = 9
• Number is 6 times the units digits
To find :
• The number
Solution :
Let the two digit number be 10x + y
where,
- 10x is the 10 digit number
- y is the unit digit
and
- x and y are the digits
According to the first condition given in the question,
→ Sum of the digits of a 2 digit number = 9
→ x + y = 9 ------(1)
According to the second condition given in the question,
→ The number = 6(Unit digit number)
→ 10x + y = 6(y)
→ 10x + y = 6y
→ 10x + y - 6y = 0
→ 10x - 5y = 0 ----(2)
Making to coefficients same of (1) and (2) :-
→ (x + y = 9) × 5
→ 5x + 5y = 45 -----(3)
→ (10x - 5y = 0) × 1
→ 10x - 5y = 0 ------(4)
Solving (3) and (4) :-
→ 5x + 5 = 45
→ 10x - 5y = 0
____________
→ 15x = 45
____________
→ 15x = 45
→ x = 45 ÷ 15
→ x = 3
→ The value of x = 3
Substitute the value of x in equation (1) :-
→ x + y = 9
→ 3 + y = 9
→ y = 9 - 3
→ y = 6
→ The value of y = 6
The original number is :-
→ 10x + y
→ 10(3) + 6
→ 30 + 6
→ 36
Therefore, the original number = 36