A can complete a work in 20 days, while B can complete the same work in 25 days. Both work together for 10 days, and then C alone completes the remaining work in 10 days. In how many days can A, B, and C together complete the same work?

Let total work = 1

Step 1: Work rates

A’s 1-day work = $1/20$
B’s 1-day work = $1/25$

Together:
$\frac{1}{20} + \frac{1}{25} = \frac{5+4}{100} = \frac{9}{100}$

Step 2: Work done in 10 days by A + B

$10 \times \frac{9}{100} = \frac{90}{100} = 0.9$

Remaining work = $1 - 0.9 = 0.1$

Step 3: C’s work

C completes $0.1$ work in 10 days

So C’s 1-day work:
$0.1 / 10 = 0.01 = 1/100$

Step 4: A + B + C together

$\frac{1}{20} + \frac{1}{25} + \frac{1}{100}$

LCM = 100:

$= 5/100 + 4/100 + 1/100 = 10/100 = 1/10$

Step 5: Time taken

Time = $1 \div (1/10) = 10$ days

Final Answer: 10 days