Water Leaks Out of the Bottom of the Tank
Problem: Water leaks out of the bottom of the tank.
Solution: There are three possibilities here. The bottom of the ball cock could be leaking, the connection between the external water-supply line and the ball cock could be loose, or the tank bolts might have corroded, causing water to seep out.
The water-supply line feeds water into the threaded ball-cock tailpiece that protrudes from the bottom of the tank. It's held in place by a jamb nut that screws up from the bottom outside of the tank. Try tightening the nut as a first step.
If that doesn't work, replace the ball cock (around $6). Unscrew the supply-line coupling and detach the line. Then unscrew the jamb nut and pull the ball cock out. Fit a new washer over the new ball cock and coat the bottom of this cone-shaped washer with Teflon pipe dope. Thread the jamb nut by hand, then tighten with a wrench. Be sure to buy an antisiphon ball cock, which prevents the backflow of contaminated wastewater.
Another possibility is that there's a leaking connection between the supply line and tailpiece. To repair the connection, unscrew the supply-tube coupling and replace the line with durable braided-stainless-steel line (around $6). Bring the old one to the store to match coupling sizes and line length. Coupling sizes are 3/8, 1/2, and 7/8 inch. Check both ends because many supply lines are 3/8 inch on one end and 1/2 inch on the other.
If the shutoff valve is leaking, replace it with a stainless-steel one for around $6.
In an older toilet, leaky tank bolts are another possible cause of a leak. First, try gently tightening the bolts (overtightening can crack the tank). If the leak persists, replace the rubber washers inside the tank or the bolts themselves if they're corroded.