Question

the sum of digits of a 2 digit no. is 5. the number formed by interchanging the digits is 9 less than the original number. find the original no

Answer 1

GIVEN

The sum of digits of a 2 digit no. is 5. the number formed by interchanging the digits is 9 less than the original number.

TO FIND

Find the original number

SOLUTION

★Let the ones digit be x then tens digit be y

Original number = 10y + x

According to the given condition

• x + y = 5 ----(i)

The number formed by interchanging the digits is 9 less than the original number.

→ 10x + y = ( 10y + x ) - 9

→ 10x + y = 10y + x - 9

→ 10x - x + y - 10y = -9

→ 9x - 9y = -9

→ 9(x - y) = -9

→ x - y = -1 ----(ii)

Add both the equations

→ (x + y) + (x - y) = 5 -1

→ x + y + x - y = 4

→ 2x = 4

→ x = 4/2 = 2

Putting the value of x in eqⁿ (ii)

→ x - y = -1

→ 2 - y = -1

→ y = 2 + 1 = 3

Hence

Original number = 10y + x = 10*3 + 2 = 32

Answer 2

ɢɪᴠᴇɴ :-

The sum of digits of a 2 digit no. is 5. the number formed by interchanging the digits is 9 less than the original number.

ᴛᴏ ғɪɴᴅ :-

• Original number

sᴏʟᴜᴛɪᴏɴ :-

Let tense place digit be x & ones place be y

Then ,

ᴄᴏɴᴅɪᴛɪᴏɴ -1 :-

• ( x + y) = 5. --(1)

Now,

➦ Original number = (10x + y)

➦ Interchanged number = (10y + x)

ᴄᴏɴᴅɪᴛɪᴏɴ -2 :-

➭ 10y + x - 9 = 10x + y

➭ 10y - y + x -10x = 9

➭ 9y - 9x = 9

➭ 9(x - y ) = 9

➭ (x - y) = 9/9

➭ ( x - y) = 1. --(2)

On adding (1) and (2) , we get,

➭ (x + y) + (x - y) = 5 + 1

➭ 2x = 6

➭ x = 6/2

➭ x = 3

Put x = 3 in (1) , we get

➭ (x + y) = 5

➭ 3 + y = 5

➭ y = 5 - 3

➭ y = 2

Hence,

• Original number(10x + y) = 32

• Interchanged number(10y + x) = 23