the sum of the digits of a 2 digits number is 7 .if the digit are reversed ,the new number increased by 3 less than 4 times of the original number. find the original number
Answers
Let the digit in ones place be x. Then the digit in tens place will be 7-x. The number is 10 (7-x) + x = 70–9x.
If the digits are reversed, the new number will be 10 x + 7- x = 9x+7.
According to the problem 9 x + 7 = 4(70–9x) -3 i.e., 9 x+7 = 277 -36 x => 45 x = 270 => x = 6.
The original number = 70–9 x = 70–54 = 16.
The new number = 9 x +7 = 54+7 = 61
Required Answer :
The original number = 16
Given :
- The sum of the digits of a 2 digits number = 7
- If the digits are reversed, the new number is increased by 3 less than 4 times of the original number.
To find :
- The original number
Solution :
Let the original number be 10x + y
where,
- 10x is the ten's digit number.
- y is the units digit number.
According to the question,
→ Sum of the digits of a two digit number = 7
→ x + y = 7 ----(1)
Number after reversing :
→ 10y + x + 3
According to the question,
→ 10y + x = 4(10x + y) - 3
→ 10y + x = 40x + 4y - 3
→ 10y - 4y = 40x - x - 3
→ 6y = 39x - 3
→ 39x - 6y - 3 = 0
→ Taking 3 common :
→ 3(13x - 2y - 1) = 0
→ 13x - 2y - 1 = 0
→ 13x - 2y = 1 -----(2)
Taking (1) and (2) :
→ (x + y = 7) × 2
→ 2x + 2y = 14 -----(3)
→ (13x - 2y = 1) × 1
→ 13x - 2y = 1 -----(4)
Solving (3) and (4) :
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀2x + 2y = 14
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀13x - 2y = 1
⠀⠀⠀⠀⠀⠀⠀⠀⠀____________
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀15x = 15
⠀⠀⠀⠀⠀⠀⠀⠀⠀____________
→ 15x = 15
→ x = 15/15
→ x = 1
Substitute the value of x in equation (1) :
→ x + y = 7
→ 1 + y = 7
→ y = 7 - 1
→ y = 6
→ The original number = 10x + y
→ The original number = 10(1) + 6
→ The original number = 10 + 6
→ The original number = 16