Question

A two digited number is such that the product of its digits is 28.
When 27 is added to this number, the digits interchange their places.Find the number.​

Answer 1

Your answer is given below =>>

Given :Let the x be th number at units place and y be the number at digits place

number will be =x+27y

Reverse number will be 27x+y

Product of digit is 28

Therefore,xy=28 -----{1}

original number + 9=reverse number

x+27y +28=27x +y

27x-27y=28

x-y=1-------{2}

using formula (x+y)²=(x-y)²+4xy

(x+y)²=(1)²+4(20) [ by using equation 1 and 2]

(x+y)²=1+80=81

(x+y)=9-----(3)

solve equation 3 and 2

x+y=9

x-y=1

_______

by adding, we get,

2x=10

⇒x=5

y=9-5

y=4

so x and y are 5 and 4

so number is x +10y =5 +10x4=5+40=45

∴Required number is 45

Answer 2

Explanation:

Given -

• Product of two digit number is 28
• When 27 is added to this number then the digit interchange their places.

To Find -

What's the number

let the two digit number be 10x+ y

Now,

According to the question :-

Product of two digit number is 28

It means,

• x × y = 28 ....... (i)

And

When 27 is added to the number then the digit interchange their places

It means,

10x + y + 27 = 10y + x

» 9y - 9x = 27

» 9(y - x) = 27

» y - x = 3

• » y = 3 + x ........... (ii)

Now,

Substituting the value of y on equation (i), we get :

» x × y = 28

» x(3 + x) = 28

» x² + 3x - 28 = 0

Now, Factorising this

By middle term splitt :-

» x² - 4x + 7x - 28

» x(x - 4) + 7(x - 4)

» (x + 7)(x - 4)

Hence,

The value of x is 4

Now,

Substituting the value of x on equation (ii), we get :

» y = 3 + x

» 3 + 4

• » 7

Hence,

The value of x is 4 and y is 7

Therefore,

The two digit number is

10x + y =

» 10(4) + 7

» 40 + 7

» 47