Question

A two-digit number is obtained either by multiplying the sum of the digits by Sand
adding 1. or by multiplying the difference of the digits by 13 and adding 2. Find the
number. How many such numbers are there?​

Answer 1

$\huge\mathfrak\red{Answer⤵}$

Let the tens digit is x and unit digit is y , the two digit number = 10.x+y , accordingly :-

8.(x+y)+1 = 10x+y. Or. -2.x + 7.y = -1……………………..(1) and

13.(x-y)+2= 10x+y. Or. 3.x - 14.y = -2……………………(2)

From eqn. (1) and (2) , x/(-14–14) =y/(-3–4) = -1/(28–21).

or, x/(-28) = y/(-7) = -1/7.

or, x= (-28)×(-1/7) = 4. and. y = (-7)×(-1/7) = 1.

Required number = 10x+y = 10×4 + 1 = 41.

Answer 2

Answer:

Let the tens digit is x and unit digit is y , the two digit number = 10.x+y , accordingly :-

8.(x+y)+1 = 10x+y. Or. -2.x + 7.y = -1……………………..(1) and

13.(x-y)+2= 10x+y. Or. 3.x - 14.y = -2……………………(2)

From eqn. (1) and (2) , x/(-14–14) =y/(-3–4) = -1/(28–21).

or, x/(-28) = y/(-7) = -1/7.

or, x= (-28)×(-1/7) = 4. and. y = (-7)×(-1/7) = 1.

Required number = 10x+y = 10×4 + 1 = 41.