The sum of the digits of a 2 digit number is 7. If the digits are reversed, the new number increased by 2 less than 4 times the original number. Find the original number. the dots is 110, and the difference of the digit is 6. find the number.
Answers
Appropriate Question:
- The sum of the digits of a 2-digit number is 7. If the digits are reversed, the new number increased by 3 less than 4 times the original number. Find the original number.
Given that:
- The sum of the digits of a 2-digit number is 7.
To Find:
- Find the original number.
Let us assume:
- Tens digit be x.
- Ones digit = 7 - x
- Original number = 10x + (7 - x)
The digits are reversed.
- New number = 10(7 - x) + x
The new number increased by 3 less than 4 times the original number.
New number = 4{Original number} - 3
↠ 10(7 - x) + x = 4{10x + (7 - x)} - 3
↠ 70 - 10x + x = 4{10x + 7 - x} - 3
↠ 70 - 9x = 40x + 28 - 4x - 3
↠ 70 - 28 + 3 = 40x - 4x + 9x
↠ 45 = 45x
↠ 45/45 = x
↠ 1 = x
↠ x = 1
Original number:
↠ 10x + (7 - x) = 10(1) + (7 - 1)
↠ 10x + (7 - x) = 10 + 6
↠ 10x + (7 - x) = 16
Hence,
- The original number is 16.
Given :-
The sum of the digits of a 2 digit number is 7. If the digits are reversed, the new number increased by 3 less than 4 times the original number. Find the original number. the dots is 110, and the difference of the digit is 6
To Find :-
Number
Solution :-
Let's assume that the digit at tens place is x and unit place is 7 - x
Now, according to the question
10(7 - x) + x = 4[10x + (7 - x)] - 3
70 - 10x + x = 4[10x + 7 - x] - 3
70 - (10x + x) = 4[(10x - x) + 7] - 3
70 - 9x = 4[9x + 7] - 3
70 - 9x = 36x + 28 - 3
70 - 9x = 36x + 25
70 - 25 = 36x + 9x
45 = 45x
45/45 = x
1 = x
Therefore
Original number
10x + 7 - x
10 × 1 + 7 - 1
10 + 7 - 1
17 - 1
16