A difficult question of Variation is ……

In a pasture, grass grows at a uniform rate per day. If 40 goats graze, the grass is exhausted in 6 days. If 20 goats graze, the grass is exhausted in 16 days. If the grass is exhausted in 12 days, find the number of goats grazing.

Try the question before watching the video, explaining the question in its entirety (traditional as well as short-cut).

Now can you get the following two questions, each question, within 1 minute?

Q. 1: It takes 24 days for 70 cows to graze a pasture completely. However if there were only 30 cows, the pasture would have lasted for 60 days. How many cows will graze the entire pasture in 96 days? Consider that grass grows at a uniform rate per day.

Q. 2: The number of bacteria in a jar grow at a constant rate per hour. To kill bacteria, antibiotics are introduced in the jar. Each ml of antibiotic added to the jar kill the bacteria at a fixed rate per hour. When 20 ml of antibiotic is poured in the jar, it takes 8 hours for all the bacteria to be killed. When 25 ml of antibiotic is poured in the jar, it takes 6 hours for all the bacteria to be killed. If 30 ml of antibiotic is poured in the, all the bacteria will be killed in how many hours?

Approaches may be discussed on answers checked in the comments.