Question

A number consist of two digit whose sum of digits is 8 if 18 is added to a number the digits interchange the place find the numbers

Answer 1

ʟᴇᴛ ᴛʜᴇ ᴅɪɢɪᴛ ᴀᴛ ᴏɴᴄᴇ ᴩʟᴀᴄᴇ ʙᴇ x
ᴛᴇɴꜱ ᴩʟᴀᴄᴇ ʙᴇ y
ᴛʜᴇ ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ= 10y+x
ᴀᴛq
x+y=8. .........(1)
ᴏɴ ʀᴇᴠᴇʀꜱᴇᴅ
ᴛʜᴇ ɴᴜᴍʙᴇʀ ɪꜱ
10x+y
10y+x+18= 10x+y
9y-9x+18=0
9y-9x=-18 ᴅᴇᴠɪᴅɪɴɢ ʙᴏᴛʜ ꜱɪᴅᴇꜱ ʙy -9
x-y=9.............(2)
ᴀᴅᴅɪɴɢ (1) ᴀɴᴅ (2)
x+y+ x-y =17
2x=17
x=17/2
ᴩᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏꜰ x ɪɴ (1)
17/2-8=-y
17-16/2=-y
1/2=-y
-1/2=y
ᴛʜᴇ ᴏʀɪɢɪɴᴀʟ ɴᴜᴍʙᴇʀ ɪꜱ
10×-1/2+17/2
-5+17/2
-10+17/2
7/2