the sum of the digit of two- digit is 15. if the number formed by reversing the digit is less than the original number by 27, find the original number
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ʟᴇᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴡɪᴛʜ ᴛᴡᴏ ᴅɪɢɪᴛꜱ ʙᴇ 10x + ʏ.
ꜱᴜᴍ ᴏꜰ ᴛʜᴇ ᴅɪɢɪᴛꜱ ɪꜱ 15.
⇒ x + ʏ = 15 ----------------- (1)
ɴᴜᴍʙᴇʀ ꜰᴏʀᴍᴇᴅ ʙʏ ʀᴇᴠᴇʀꜱɪɴɢ ᴛʜᴇ ᴅɪɢɪᴛꜱ = (10ʏ + x)
(10x + ʏ) - (10ʏ + x) = 27
⇒ 9x - 9ʏ = 27
⇒ x - ʏ = 3 ----------------- (2)
ꜱᴏʟᴠɪɴɢ ᴇQᴜᴀᴛɪᴏɴꜱ (1) ᴀɴᴅ (2), ᴡᴇ ɢᴇᴛ x = 9 ᴀɴᴅ ʏ = 6.
ᴛʜᴇʀᴇꜰᴏʀᴇ, ᴛʜᴇ ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ ɪꜱ 10(9) + 6 = 96.
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refer pic above please
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