Question

A two-digit number is obtained by either multiplying the sum of the digits by 8 andthen subtracting 5 or by multiplying the difference of the digits by 16 and thenadding 3. Find the number.​

Answer 1

Let ten's digit number be M and one's digit be N.

A two-digit number is obtained by either multiplying the sum of the digits by 8.

Two digit number = 10M + N

Sum of digits = M + N

According to question,

⇒ 10M + N = 8(M + N) - 5

⇒ 10M + N = 8M + 8N - 5

⇒ 10M - 8M + N - 8N = - 5

⇒ 2M - 7N = - 5 ___ (eq 1)

The difference of the digits by 16 and then by adding 3.

⇒ 10M + N = 16(M - N) + 3

⇒ 10M + N = 16M - 16N + 3

⇒ 10M - 16M + N + 16N = 3

⇒ - 6M + 17N = 3 ___ (eq 2)

Now, Multiply (eq 1) with 3

⇒ 2M - 7N = - 5 (×3)

⇒ 6M - 21N = - 15 ___ (eq 3)

Add (eq 2) from (eq3)

⇒ - 6M + 17N + 6M - 21N = 3 + (-15)

⇒ - 4N = - 12

⇒ 4N = 12

⇒ N = 3

Substitute value of N in (eq 1)

⇒ 2M - 7(3) = - 5

⇒ 2M - 21 = - 5

⇒ 2M = 16

⇒ M = 8

So,

Number :- 10M + N

⇒ 10(8) + 3

⇒ 80 + 3

⇒ 83

Answer 2

$\huge\sf{Answer:-}$

Given question:-

A two-digit number is obtained by either multiplying the sum of the digits by 8 andthen subtracting 5 or by multiplying the difference of the digits by 16 and thenadding 3.

To Find:-

Find the number.

Hence..

Let x be the 10th number and let y be the 1st number.

•♦• 10x + y = 2 digit number.

•♦• x + y = sum of digit.

So,

= 10x + y = 8 ( x + y ) - 5

= 10x 3 y = 8x + 8y - 5

= 10x - 8x + y - 8y = -5

= 2x - 7y = -5 – Equation (1)

Then,

= 10x + y = 16 (x + y ) - 3

= 10x + y = 16x - 16y + 3

= 10x - 16x + y + 16y = 3

= -6x + 17y = 3 – Equation (2)

Now , we have to multiply Equation (1) with number 3.

= 2x - 7y = -5 multiply ( × 3)

= 6x - 21y = -15 – Equation (3)

Hence, now adding Equation (2) from Equation (3)

= - 6x + 17y + 6x - 21y = 3 + ( - 15)

= 4y = -12

= 4y = 12

= (y = 3)

Substituting values of y in Equation (1)

= 2x - 1 ( 3 ) = -5

= 2x - 21 = -5

= 2x = 16

Hence,

10x + y is the number.

So,

➟ 10 ( 8 ) + 3

➟ 80 + 3

➟ 83

Therefore, 83 is the answer!