Question

the sum of two digit number and the number obtained by reversing its digits is 110 if ten is subtrated from first number, the new number is 4 more than five times first number so find the first number​

Answer 1

ʜᴇʀᴇ ɪs ʏᴏᴜʀ sᴏʟᴜᴛɪᴏɴ

ʟᴇᴛ ᴛʜᴇ ᴅɪɢɪᴛ ᴀᴛ ᴏɴᴇs ᴘʟᴀᴄᴇ = ʏ

ʟᴇᴛ ᴛʜᴇ ᴅɪɢɪᴛ ᴀᴛ ᴛᴇɴs ᴘʟᴀᴄᴇ = x

ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ = 10x + ʏ 

ɴᴜᴍʙᴇʀ ғᴏʀᴍᴇᴅ ʙʏ ʀᴇᴠᴇʀsɪɴɢ ᴛʜᴇ ᴅɪɢɪᴛs =10ʏ + x

ᴏɴ ᴀᴅᴅɪɴɢ ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ ᴀɴᴅ ʀᴇᴠᴇʀsᴇᴅ ɴᴜᴍʙᴇʀ.

10x+ʏ+10ʏ+x = 110

11x + 11ʏ = 110

11 (x + ʏ ) = 110

x + ʏ = 10

x = 10 - ʏ ................................................. (1)

ᴏɴ sᴜʙᴛʀᴀᴄᴛɪɴɢ 10 ғʀᴏᴍ ᴛʜᴇ ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ , ᴡᴇ ɢᴇᴛ = 10x + ʏ -10

ᴀɴᴅ

4 ᴍᴏʀᴇ ᴛʜᴀɴ 5 ᴛɪᴍᴇs ᴛʜᴇ sᴜᴍ ᴏғ ᴅɪɢɪᴛs = 5(x + ʏ) + 4

ᴀ/ϙ

 

10x + ʏ -10 = 5(x + ʏ) + 4

10x + ʏ -10 = 5x +5ʏ + 4

10x -5x + ʏ -5ʏ = 10 +4

5x - 4ʏ = 14.................................................. (2)

ᴘᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ x ɪɴ ᴇϙᴜᴀᴛɪᴏɴ (2)

5x - 4ʏ = 14

5×(10-ʏ) - 4ʏ = 14

50-5ʏ-4ʏ =14

-9ʏ = 14 -50

-9ʏ = -36

ʏ = 4

ɴᴏᴡ

x = 10-ʏ

x = 10 - 4

x = 6

ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ ᴏʀ ғɪʀsᴛ ɴᴜᴍʙᴇ = 10x + ʏ  = 10×6+4 = 64

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ....