Question

A two digit no is obtained by either multiplying no by 8 and adding 1 or multiplying the difference of digit's by 13 and adding 2 find the number​

Answer 1

EXPLANATION.

• GIVEN

A two digit number is obtaining by either

multiplying number by 8 or adding 1 .

Multiplying the difference of digit by 13 and

adding 2 .

Find the number.

According to the question,

Let the digit at ten's place = x

Let the digit at unit place = y

original number = 10x + y

reversing number = 10y + x

case = 1

=> 10x + y = 8 ( x + y) + 1

=> 10x + y = 8x + 8y + 1

=> 2x - 7y = 1 .......(1)

case = 2

=> 10x + y = 13 ( x - y) + 2

=> 10x + y = 13x - 13y + 2

=> - 3x + 14y -2 = 0

=> 3x - 14y = - 2 ........(2)

From equation (1) and (2) we get,

multiply equation (1) by 2

multiply equation (2) by 1

we get,

=> 4x - 14y = 2

=> 3x - 14y = -2

we get,

=> x = 4

put the value of x = 4 in equation (1)

we get,

=> 2(4) - 7y = 1

=> 8 - 7y = 1

=> -7y = -7

=> y = 1

Therefore,

Number are = 10x + y = 10(4) + 1 = 41

Number are = 41

Answer 2

Step-by-step explanation:

$\bf {\underline {\underline \red{Given:-}}}$

• A two digit number obtained by either multiplying the sum of digits by 8 and adding 1

• Or it can be obtained by multiplying the difference of digits by 13 and adding 2

$\bf {\underline {\underline \blue{To\:Find:-}}}$

• The number.

$\bf {\underline {\underline \green{Solution:-}}}$

Let the tens digit be x

And the units place digit be y

The number = 10x + y

According to the 1st condition :-

$\sf \longrightarrow10x + y = 8(x + y) + 1$

$\sf \longrightarrow10x + y = 8x +8 y + 1$

$\sf \longrightarrow10x - 8x+ y - 8y= 1$

$\sf \longrightarrow2x- 7y= 1.......(i)$

According to the 2nd condition :-

$\sf \longrightarrow10x + y = 13(x - y) + 2$

$\sf \longrightarrow10x + y = 13x - 13y + 2$

$\sf \longrightarrow10x - 13x+ y + 13y= 2$

$\sf \longrightarrow- 3x+ 14y= 2......(ii)$

Now,Adding equation (i) and (ii)

• 2x - 7y = 1

• -3x + 14y = 2

Multiply equation (i) with 2

→ 2(2x - 7y = 1)

→ 4x - 14y = 2

Now add 4x - 14y = 2 and -3x + 14y = 2

4x - 14y = 2

-3x + 14y = 2

____________

x = 4

Substitute x = 4 in equation (i)

→ 2(4) - 7y = 1

→ 8 - 7y = 1

→ -7y = -7

→ y = 1

Number = 10x + y

10(4) + 1 = 41

Hence;

$\boxed{ \rm \therefore The \: number \: = 41}$