Question

A number consists of two digits whose sum is
8.If 18 is added to the number, its digits are
interchanged. The number is​

Answer 1

GIVEN

A number consists of two digits whose sum is 8.If 18 is added to the number, its digits are interchanged.

TO FIND

Find the number

SOLUTION

★Let the ten's digit of required number be x and one's digit be y

✞ According to the given condition

• x + y = 8 ---(i)

Required number = (10x + y)

Number obtained by interchanging

= (10y + x)

• (10x + y) + 18 = (10y + x)

→ 10x + y + 18 = 10y + x

→ 10x - x + y - 10y = -18

→ 9x - 9y = -18

→ 9(x - y) = -18

→ x - y = -2 ----(ii)

✞ Add both the equations

→ (x + y)+(x - y) = 8 - 2

→ x + y + x - y = 6

→ 2x = 6

→ x = 6/2 = 3

✞ Putting the value of x in eqⁿ (ii)

→ x - y = -2

→ 3 - y = -2

→ y = 3 + 2 = 5

✬ Required number

= (10x + y)

= (10*3 + 5) = 30 + 5 = 35

Hence, the required number is 35

Answer 2

Gɪᴠᴇɴ:-

A number consists of two digits whose sum is 8.If 18 is added to the number, its digits are interchanged.

Tᴏ ғɪɴᴅ :-

• Number

sᴏʟᴜᴛɪᴏɴ :-

➦ Let Tens place digit be x & Ones place be y

Then,

➭ ( x + y) = 8

➭ x = 8 - y. ---(1)

Now,

➦ Original number = 10x + y

➦ Interchanged number = 10y + x

➭ (10x + y) + 18 = (10y + x)

➭ 10x + y + 18 = 10y + x

➭ 10x - x + y - 10y = -18

➭ 9x - 9y = -18

➭ 9( x - y) = -18

➭ (x - y) = -18/9

➭ x - y = -2. --(2)

Put the value of (1) in (2) , we get,

➭ ( 8 - y) - y = -2

➭ 8 - 2y = -2

➭ -2y = -2 - 8

➭ -2y = -10

➭ y = -10/-2

➭ y = 5

Put y = 5 in (1) , We get,

➭ x + y = 8

➭ x + 5 = 8

➭ x = 8 - 5

➭ x = 3

Hence,

• Ones place digit = x = 3

• Tens place digit = y = 5

therefore,

➦ Original Number = 10x + y = 10×3 + 5 = 35

➦ Interchanged number = 10y + x = 10×5 + 3 = 53

Therefore,

• Original No = 35

• Interchanged No = 53