Sino-Korean has no special words for eleven, twelve or the teens. Every number up to 99 is built from day 1's ten syllables: the number of tens, then 십, then the units. Today covers the pattern, the joins where the sound changes, and the numbers you will meet on buses and in banks.
The pattern
Every two-digit number fills the same three slots:
How many tens
이
i
two
Ten
십
sip
ten
Units
오
o
five
Said as one word
이십오
isibo
twenty-five
The same with nines
구십구
gusipgu
ninety-nine
Why it works
Sino-Korean numbers are arithmetic said aloud. 이십 is 'two ten', twenty, and 이십오 is 'two ten five'. English hides the same structure behind eleven, twelve, the teens and words like 'fifty', which have to be memorised one by one, while a Korean child who can count to ten can say every number to ninety-nine. For the teens there is nothing in front of 십, so eleven is 십일 'ten one': a single ten needs no counting, and day 3 shows the same thing happening with hundreds.
Where the joins change
Written, a number is its syllables in a row. Said, the joins behave like the joins inside any Korean word:
eleven
Syllable by syllable
십일
sip-il
Said
[시빌]
sibil
The ㅂ of 십 slides into the empty block of 일. 십오 'fifteen' does the same: [시보], sibo.
sixteen
Syllable by syllable
십육
sip-yuk
Said
[심뉵]
simnyuk
An n sound appears in front of 육, and the ㅂ turns into m before it. Twenty-six, 이십육, is [이심뉵].
sixty
Syllable by syllable
육십
yuk-sip
Said
[육씹]
yuksip
After the k of 육 the ㅅ is said tense. Romanisation does not show this, so it stays yuksip.
fifty-one
Syllable by syllable
오십일
o-sip-il
Said
[오시빌]
osibil
The same linking as 십일, now inside a longer number.
Why it works
A number said aloud is one word, so the ordinary rules for joins inside Korean words apply to it. Linking moves a final consonant into an empty block, which opens 십일 and 십오 up to si-bil and si-bo. 십육 is the odd one: when a syllable ending in a consonant meets one starting with a y sound, Korean often slips in an n, which turns 육 into [뉵], and that n then pulls the ㅂ before it into m. Among two-digit numbers only 육 does this, so sixteen, twenty-six and so on up to ninety-six are the only ones to watch.
Numbers you will hear
Four everyday uses, all with this set:
삼십 분
samsip bun
thirty minutes
분 is minute, as in day 1's 오 분.
칠십오 번 버스
chilsibo beon beoseu
the number 75 bus
번 is number and 버스 is bus. The ㅂ of 십 links forward: chil-si-bo.
사십이 번
sasibi beon
number 42
Banks and clinics hand out numbered tickets and call them like this, often with 고객님 (gogaengnim), 'customer', after it.
이십 대
isip dae
in your twenties
대 is a decade of life. Age in years takes the native set, but the decade takes this one: 삼십 대, in your thirties.
Why it works
Each of these is a label or a measurement, the job this set was given on day 1. Bus numbers and ticket numbers are names; minutes are measured. 이십 대 shows the two systems sharing one subject: someone who is 스물다섯 살, twenty-five in native numbers, is 이십 대, in their twenties, in Sino-Korean ones. Day 5 explains the native half and day 12 comes back to age.