A two digit number is obtained by either multiplying sum of digits by 8 and adding 1 or by multiplying the difference of digits by 13 and adding 2. find the number
Answers
Answer:
Step-by-step explanation:
10x+y=8(x+y)+1
10x+y=8x+8y+1
2x-7y=1 -- *1
10x+y=13(x-y)+2
10x+y=13x-13y+2
3x-14y=-2 ---*2
(*1) * 2; 4x-14y=2--*3
*3-*2; x=4
So, y=1
Hence the number is 41
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Given:-
- A two digits number is obtained by multiplying sum of digits by 8 and then adding 1 to it.
- A two digits number of obtained by multiplying the difference of digits by 13 and adding 2.
To find:-
- Find the original number.?
Solutions:-
- Let the digits at ten's place be x.
- Let the digits at one's place be y.
Number = 10x + y
A two digits number is obtained by multiplying sum of digits by 8 and then adding 1 to it.
Sum of digits = x + y
According to the questions;
=> 10x + y = 8(x + y) + 1
=> 10x + y = 8x + 8y + 1
=> 10x + y - 8x -8y - 1 = 0
=> 2x - 7y - 1 = 0
=> x = 7y - 1/2 ...........(i).
A two digits number of obtained by multiplying the difference of digits by 13 and adding 2.
Difference of digits = x - y
According to the questions;
=> 10x + y = 13(x - y) + 2
=> 10x + y = 13x - 13y + 2
=> 13x - 13y + 2 - 10x - y = 0
=> 3x - 14y + 2 = 0 .............(ii).
Putting the value of x in Eq. (ii).
=> 3x - 14y + 2 = 0
=> 3( 7y - 1/2) - 14y + 2 = 0
=> 21y + 3/2 - 14y + 2 = 0
=> 21y + 3 - 28y + 4/2 = 0
=> -7y + 7/2 = 0
=> 7y = 7
=> y = 7/7
=> y = 1
Putting the value of y in Eq (ii)
=> 3x - 14y + 2 = 0
=> 3x - 14 × 1 + 2 = 0
=> 3x - 14 + 2 = 0
=> 3x - 12 = 0
=> 3x = 12
=> x = 12/3
=> x = 4
So, Number => 10x + y
= 10 × 4 + 1
=> 40 + 1
=> 41.