Question

A number has 2 digits whose sum is 7 if 27 is added ti number its digits get interchanged

Answer 1

given :

the no. has 2 digits






let ,

the 1st digit = x ( unit's place )

the 2nd digit = y ( tense place )




the no. can be represented as

10 × y + x

because ,

suppose a no. 52 :

5 × 10 + 2




the no. formed after interchange :

10 × x + y





from the given condition ,

x + y = 7





10 × y + x + 27 = 10 × x + y

10 y - y + 27 = 10x - x

9y + 27 = 9x

9x - 9y = 27

x - y = 3





add both equations :

x + y = 7
+
x - y = 3
_______

2x = 10

$x = \frac{10}{2} \\ \\ x = 5$


put x = 5 in equation 1 ,

x + y = 7

5 + y = 7

y = 2








the no. :

10 × y + x

2 × 10 + 5

20 + 5

25

Answer 2

Answer:

X=2 y= 5

Step-by-step explanation:

Let x be the tenth digit y be the one digit

So 10x +y = number

Given x+y = 7 (1)

And 10x +y +27= 10y + x

9x -9y =-27

X-y =-3 (2)

Solving (1) and (2)

Y gets cancelled in addition of the equations giving x= 2

Substituting x value in (1)

Y= 5

All the best ☺