Question

7. A two digit number is such that the product of
digits is 12. When 36 is added to this number, ti
digits interchange their places. Find the number,​

Answer 1

Answer:

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Step-by-step explanation:

Let the ten's digit be x and unit's digit be y.

Number = 10x + y

xy = 12  ⇒ y = 12/x … (i)

Also, 10x+y+36 = 10y+x

9x-9y+36 = 0

x-y+4 = 0 … (ii)

From (i) and (ii),

x+4 = 12/x

x^2+4x-12=0

(x+6)(x-2) =0

x=2 or x=-6

Rejecting x = -6, we have x = 2.

y=12/x =12/2=6

Thus, the required number is 2 x 10 + 6 = 26.

Answer 2

Step-by-step explanation:

Let a digit at unit’s place be x and at ten’s place by y .

Then according to problem

Required no. = 10y + x

On interchanging the digits

Number formed = 10x + y

xy =  12

∴   x = 12/y

10y + x + 36 = 10x + y

10y + x – 10x – y   =   - 36

9y – 9x = - 36

9(y – x) = - 36

y – x  =  - 36/9

y – x =  - 4

On  substituting value of  x = 12/y

y -  12/y = - 4

y2 – 12/y = - 4

y2 + 4y – 12 = 0

y2 + 6y – 2y – 12 = 0

y(y + 6) – 2(y + 6) = 0

( y + 6)(y – 2) = 0

y  =   - 6, 2

When   y = 2

x =  12/2 = 6

Required  no. = 10y + x

= 10 × 2 + 6

= 20 + 6

 = 26