Problem 1:

If both cold and hot leak together (t), the time taken would be less
than either cold (c) or hot (h).

So, we can form the inequality 0 < t < c < h

We can hence conclude I is true and II is false

If c = h, then t = c/2 = h/2. But we know c < h, so t has to be > c/2 and
less than h/2. So, III is true.

So, E -- I and III only.

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Problem 2:

(1001+999)(1001-999) / (101+99)(101-99)
= 2000*2 / 200*2
= 10

Love the crystal-clear explanations. Thanks a bunch!