6.
The sum of digits of a 2-digit number
is 6 If the digits of the numbers are reversed
the new number is decreased by 36 find the
number.
Answers
Answered by
18
Given :-
- The sum of digits of a 2-digit number is 6 If the digits of the numbers are reversed the new number is decreased by 36
To find :-
- Original number
Solution :-
Let the ones digit be y then tens digit be x
- Original number = (10x + y)
According to the first condition
- Sum of digits of a 2-digit number is 6
→ x + y = 6 -----(i)
According to the second condition
- The digits of the numbers are reversed
- the new number is decreased by 36
- Reversed number = (10y + x)
→ 10x + y = 10y + x - 36
→ 10x + y - 10y - x = - 36
→ 9x - 9y = - 36
→ 9(x - y) = - 36
→ x - y = - 4 -------(ii)
Add both the equations
→ (x + y) + (x - y) = - 4 + 6
→ x + y + x - y = 2
→ 2x = 2
→ x = 2/2 = 1
Put the value of x in equation (ii)
→ x - y = - 4
→ 1 - y = - 4
→ y = 1 + 4 = 5
Therefore ,
- Tens digit = x = 1
- Ones digit = y = 5
Hence,
- Original number = 10x + y = 15
- Reversed number = 10y + x = 51
Similar questions