Math, asked by pabhishek4076, 11 months ago

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

Answered by aadhikailash24
2

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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Answered by silentlover45
5

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.

Hence, the original number is 41.

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