Question

the sum of digits of a two-digit number is 15.if the new number formed by changing the places of the digits is greater tgan the original number by 9,find the original number and check the solution also.​

Answer 1

Answer:

• let the tenth digit be a

• and unit' digit be b,

• then the number is 10a+b.

According to question

sum of two digits is 15

a+b=15

a+b-15=0_________(1)

And

changing the digits the new number

formed greater than the original

number by 9

10b+a=10a+b+9

9a-9b+9=0

9(a-b+1)=0

a-b+1=0_________(2)

now adding equations (1) and (2)

a+b-15+a-b+1=0

2a-14=0

2a=14

a=14/2

a=7.

substitute a value in equation (1)

7+b-15=0

b-8=0

b=8.

therefore the number is 10a+b

10×7+8=70+8=78.

verification:

the original number is 78

so,

according to question

sum of the digits is 15

7+8=15 (verified)

and if interchange the digits the new

number formed greater than the

original number by 9

87=78+9.

Hence proved.