Question

The sum of the digit of a two digit no. is 15. The number obtained by intercharging its digit exceeds the given no. by 9 . Find the original number

Answer 1

☆ɢɪᴠᴇɴ :-

ꜱᴜᴍ ᴏꜰ ᴅɪɢɪᴛꜱ ᴏꜰ ᴀ ᴛᴡᴏ-ᴅɪɢɪᴛ ɴᴜᴍʙᴇʀꜱ ɪꜱ 15.ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏʙᴛᴀɪɴᴇᴅ ʙʏ ɪɴᴛᴇʀᴄʜᴀɴɢɪɴɢ ɪᴛꜱ ᴅɪɢɪᴛꜱ ᴇxᴄᴇᴇᴅꜱ ᴛʜᴇ ɢɪᴠᴇɴ ɴᴜᴍʙᴇʀ ʙʏ 9.

☆ᴛᴏ ꜰɪɴᴅ :-

ᴛʜᴇ ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ

☆ꜱᴏʟᴜᴛɪᴏɴ :-

ʟᴇᴛ ᴛʜᴇ ᴛᴇɴꜱ ᴅɪɢɪᴛ ɴᴜᴍʙᴇʀ ʙᴇ x

ᴀɴᴅ ᴛʜᴇ ᴜɴɪᴛꜱ ᴅɪɢɪᴛꜱ ɴᴜᴍʙᴇʀ ʙᴇ ʏ

ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ = (10x + ʏ)  

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ Qᴜᴇꜱᴛɪᴏɴ

1ꜱᴛ ᴇQᴜᴀᴛɪᴏɴ

x + ʏ = 15 ……..(ɪ)  

2ɴᴅ ᴇQᴜᴀᴛɪᴏɴ

ɴᴜᴍʙᴇʀ ᴏʙᴛᴀɪɴᴇᴅ ᴏɴ ʀᴇᴠᴇʀꜱɪɴɢ ɪᴛꜱ ᴅɪɢɪᴛꜱ = (10ʏ + x)  

⇒ (10ʏ + x) = (10x + ʏ) + 9  

⇒ 10ʏ + x – 10x – ʏ = 9  

⇒ 9ʏ – 9x = 9  

⇒ ʏ – x = 1 …….(ɪɪ)  

ᴏɴ ᴀᴅᴅɪɴɢ (ɪ) ᴀɴᴅ (ɪɪ)

⇒ 2ʏ = 16  

⇒ ʏ = 8  

ᴘᴜᴛᴛɪɴɢ ᴀʟʟ ᴛʜᴇ ᴠᴀʟᴜᴇꜱ ɪɴ ᴇQ (ɪ)

⇒ x + ʏ = 15

⇒ x + 8 = 15  

⇒ x = (15 – 8)

⇒ x = 7  

ɴᴜᴍʙᴇʀ = (10x + ʏ)

= 10 × 7 + 8

= 70 + 8

= 78  

ʜᴇɴᴄᴇ, ᴛʜᴇ ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ ɪꜱ 78.