Question

The sum of the digits of a two - digit number is 15. if the digits are interchanged, then the new number is 27 lesser than the original number. find the original number.​

Answer 1

Answer:

96

Step-by-step explanation:

let consider the number is 10x+y

then (x+y)=15

again (10x+y)-(10y+x)=27

9x-9y=27

x-y=3

so the value of x is 9 and the value of your is 6

thus the answer is 96

Answer 2

Answer:

ORIGINAL NUMBER = 96

Step-by-step explanation:

given that,

The sum of the digits of a two - digit number is 15

le the digits be x and y

so

the numvers be,

10y + x.

now,

according to the question,

x + y = 15. ....(1)

also,

given that,

if the digits are interchanged, then the new number is 27 lesser than the original number.

so,

interchanged digit number

= 10x + y

so,

according to the question,

10y + x = 10x + y + 27

10y - y + x - 10x = 27

9y - 9x = 27

9(y - x) = 27

y - x = = 27/9

y - x = 3. ...(1)

now,

we have,

y + x = 15. ....(1)

y - x = 3. .....(2)

(1) - (2)

y + x - (y - x) = 15 - 3

y + x - y + x = 12

2x = 12

x = 12/2

x = 6

putting the value of

x on (2)

y - x = 3

y - 6 = 3

y = 3 + 6

y = 9

x = 6

so,

original number

= 10y + x

putting the values,

10(9) + 6

90 + 6

= 96

SO,

ORIGINAL NUMBER = 96