Question

sum of the digits of two digit number is 6 when we interchange the digits it is found that the resulting new number is greater than the original number by 24 what is the two digit number?​

Answer 1

Cᴏʀʀᴇᴄᴛ Qᴜᴇsᴛɪᴏɴ :-

Sum of the digits of two digit number is 6 when we interchange the digits it is found that the resulting new number is greater than the original number by 18.

ᴛᴏ ғɪɴᴅ :-

• Original Number
• Interchanged number

sᴏʟᴜᴛɪᴏɴ :-

Let tens place digit be x & ones place digit be y

Then,

According to 1st condition :-

• Sum of digits = 6

• ( x + y) = 6

• x = (6 - y) ----(1)

According to 2nd Condition :-

Now,

• Original number = (10x + y)

• Interchanged number = (10y + x)

➮ 10x + y + 18 = 10y + x

➮ 10x - x + y - 10y = -2

➮ 9x - 9y = -18

➮ 9(x - y) = -18

➮ x - y = -18/9

➮ x - y = -2 ----(2)

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

➮ (x + y) + (x - y) = 6 - 2

➮ 2x = 4

➮ x = 2

Put x = 2 in (1) , we get,

➮ x + y = 6

➮ 2 + y = 6

➮ y = 6 - 2

➮ y = 4

Hence,

• Original number(10x + y) = 24

• Interchanged number (10y + x) = 42