For Q29, the longest possible distance between A and D is when A to D is placed on a straight line.

A to B, B to C and C to D must all be on the same straight line.

A to B can be 4.94999... (which we can just say is 4.95; in the usual sense this should not be rounded down, but because 4.95 comes from 4.94999..., we call this number 4.95 the upper bound of the rounding off to 4.9).

Similarly, B to C can be 4.94999..., which we will shorten to the upper bound 4.95.

Similarly, C to D can be 9.34999..., which we will shorten to the upper bound 9.35.

Greatest length between A and D
= 4.95 + 4.95 + 9.35
= 19.25 km

For Q30,

You must know that the sum of the first few numbers (i.e. 1 + 2 + 3 + 4 + 5 + ...) is given by

Largest number * (largest number + 1) / 2

Here, I see 1, 2, 3, ..., 21, so the total sum of numbers from 1 to 21 is 21 * 22 / 2 = 231.

So, 1/1000 + ... is equal to 231/1000.

For Q25, we just subtract 1/3 from 4/7.

Rope left
= 4/7 - 1/3
= 12/21 - 7/21
= 5/21

Note that the questuon said "he used 1/3 metres of...".

Had the question asked "he used 1/3 of..." without the word metre. our answers would be entirely different from the given question.

Dear Gurus,
Answer for Q29 and 30 is wrong as per answer sheet.

Cannot be the case.

For Q30, I have manually added the 21 terms together a moment ago and I still got 231/1000.

For Q29, we cannot say that 4.9 comes from the rounding of 4.94, because 4.949 for example is possible. If you add 4.949, 4.949 and 9.349, for example, you get 19.247, which still rounds off to 19.25.

I’m pretty certain the answer sheet itself has mistakes.

Dear Guru,
Thank you for ensuring the answer, I also thought the answer sheet is mistake but for q30 I got 220/1000.