Nitin is 7 ranks ahead of Joginder in a class of 39. If Joginder’s rank is 17th from the last, what is Nitin’s rank from the beginning?

Question

UnlockIAS · Accepted Answer

Correct — D, 16th. Take the two facts in the order the stem supplies them. Joginder stands 17th from the last in a class of 39, so counting from the beginning he is 39 - 17 + 1 = 23rd. The +1 is not decoration: Joginder is himself counted once in the 17 and once again in the 39, so plain subtraction discards him from one of the two runs and lands you one place short. Nitin is 7 ranks ahead of Joginder, and in a rank order 'ahead' means nearer the top, so you subtract: 23 - 7 = 16th from the beginning. A second route never converts Joginder at all. Nitin sits 7 places further from the last end than Joginder does, so Nitin is 17 + 7 = 24th from the last, and 39 - 24 + 1 = 16th from the beginning. That is the route the Commission itself set out on 31 October 2025 when it disposed of the objections filed against this item, and the fact that two independent routes land on the same number is the real safety net — an off-by-one slip almost never survives being made from both ends at once. Then close with the gap test: Joginder is 23rd, Nitin is 16th, and 23 - 16 = 7, exactly the separation the stem states. Notice how tightly the paper-setter has packed the choices — 15th, 16th, 17th and 18th, every one of them within two places of the truth. Nothing in this item rewards understanding the situation; the mark turns entirely on whether the 1 was added to the right number at the right moment, which is why writing the identity down before touching any arithmetic is worth more than speed.

Why the other options are wrong — (a) This is Joginder's own figure, 17, lifted straight off the page and re-labelled as Nitin's rank from the opposite end — the commonest failure on ranking items, because 17 is the only number in the stem that looks like a rank. Test it: if Nitin were 17th from the beginning, the gap to Joginder's 23rd would be 6 ranks, not the 7 the question specifies. It is also what you get by subtracting 7 from Nitin's from-the-last position, 24 - 7 = 17, which mixes the two reference ends inside a single calculation.  (b) The classic dropped +1, and two different careless routes deliver it. Either you compute Nitin as 24th from the last and then write 39 - 24 = 15 without restoring the 1, or you convert Joginder as 39 - 17 = 22 and take 22 - 7 = 15. Both count Nitin, or Joginder, out of one of the two runs. The gap test exposes it at once: 23 - 15 = 8 ranks, one more than the 7 stated, and 15 + 24 = 39 rather than the 40 that any two counts of the same student in a class of 39 must add to.  (c) This is 17 + 1 — the +1 correctly remembered but attached to the wrong number, applied to Joginder's printed rank instead of to the difference 39 - 24. It is also the answer of a candidate who converts Joginder properly to 23rd and then subtracts 5 instead of 7. Either way the gap test kills it: 23 - 18 = 5 ranks between the two, well short of the stated 7, and 18 + 24 = 42, which no pair of end-counts in a 39-strong class can produce.

Concept: Every ranking and row-position question in an Indian state-service paper rests on one identity: for n people standing in a single ordered line, a person's position from the front plus that same person's position from the back equals n + 1. The extra 1 exists because the person is counted once in each of the two runs, so the two counts overlap by exactly one place — the same inclusive-counting effect that makes a fence of 10 posts have 9 gaps. Rearranged, position from the front = n - position from the back + 1, which converts any count given from one end into a count from the other. Three standard variants are built on it, and BPSC has used all three across cycles. First, one person and one end-count, asking for the other end-count: apply the identity directly. Second, one person and both end-counts, asking for the class strength: n = a + b - 1, subtracting the double count instead of adding it. Third, the version on this paper — two people, a stated separation, and a single end-count — where you convert once, then move along the line by the stated gap. The direction of that move is fixed by language, not by arithmetic: 'ahead of', 'above', 'better than' and 'senior to' all mean a smaller rank number, while 'behind', 'below' and 'after' mean a larger one. Everything else in the topic is bookkeeping.

State PCS 2025 Q6 — Science & Technology PYQ with Answer

State PCS 2025 Q6 — Science & Technology PYQ with Answer