Question

the sum of the digit of two digit number is 14. if the no. formed by reversing the digits is less than the original no. by 18.find the original no.

Answer 1

Gɪᴠᴇɴ :-

The sum of the digit of two digit number is 14. if the no. formed by reversing the digits is less than the original no. by 18.

ᴛᴏ ғɪɴᴅ :-

• Original number
• Reversed number

sᴏʟᴜᴛɪᴏɴ :-

Let tens place digit be x and ones place be y

then,

According to 1st condition :-

• Tens place digit + Ones place digit = 14

• (x + y) = 14. ---(1)

According to 2nd condition :-

➦ Original number = (10x + y)

➦ Reversed number = (10y + x)

• Original no = Reversed no + 18

→ (10x + y) = (10y + x) + 18

→ 10x - x + y - 10y = 18

→ 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) = 14 + 2

→ 2x = 16

→ x = 16/2

→ x = 8

Put x = 8 in (1) , we get,

→ x + y = 14

→ 8 + y = 14

→ y = 14 - 8

→ y = 6

Hence,

• Ones place digit = x = 8
• Tens place digit = y = 6

Therefore,

• Original number = 10x + y = 86
• Reversed number = 10y + x = 68