Rahul is 3 times as old as Seema. Laxmi was twice as old as Rahul four years ago. In four year’s time, Rahul will be 31. What are the present ages of Seema and Laxmi?

Question

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Correct — D, 9, 50. Anchor on the only age in the question that is pinned to a number and work outwards from it. Rahul will be 31 in four years, so Rahul is 31 − 4 = 27 today. Rahul is three times as old as Seema, so Seema is 27 ÷ 3 = 9. Four years ago Rahul was 27 − 4 = 23, and Laxmi was then twice that, namely 46; carry her forward by the same four years and Laxmi is 46 + 4 = 50 today. The Commission set out this working itself when it disposed of the objections to the paper on 31 October 2025, writing Rahul as x and Seema as y with x = 3y, Laxmi as z with z − 4 = 2(x − 4), and the third sentence as x + 4 = 31. Three equations in three unknowns look like a simultaneous system, but they are triangular: one equation contains a single unknown, and each of the other two then falls out by plain substitution, so no elimination is ever needed. Verify against all three sentences before ticking, because a wrong tick costs one-third of a mark — 27 is three times 9, four years ago 46 was twice 23, and 27 + 4 is 31. Two features of the option set are worth noticing. Three of the four choices give Seema as 9, so the first line of work eliminates only option (a) and the mark is actually decided by Laxmi. And Laxmi's present age reduces to 2x − 4, twice Rahul's present age minus four, so an error of a single year in Rahul moves Laxmi by two years — 27 gives 50 while 28 gives 52, which is exactly where the near-miss option comes from.

Why the other options are wrong — (a) Laxmi is right but Seema is not, and the slip is a specific one: 10 is what you get by dividing Rahul's future age by three, since 31 ÷ 3 is 10.3 rounded down, instead of dividing his present age 27. Rahul is 27, and three times 10 is 30, not 27, so only 9 satisfies Rahul = 3 × Seema. This is the one option a candidate can kill from the very first line of working, which is precisely why it sits at the top of the list.  (b) Seema is right but Laxmi is not, and 52 is the signature of a one-year error in Rahul. Because Laxmi's present age is 2x − 4, taking Rahul as 28 rather than 27 — the off-by-one that comes from counting 'in four years' time' inclusively — doubles into a two-year error and yields exactly 52. Tested directly, a Laxmi of 52 would have been 48 four years ago, and 48 is twice 24, whereas Rahul was 23 then.  (c) Seema is right but Laxmi is not, and 45 is unreachable by any consistent reading: since Laxmi must equal 2x − 4, a present age of 45 would require Rahul to be 24.5. Its real job is to catch the candidate who computes Laxmi's age four years ago, 46, correctly and then never brings her back to the present — 45 is the nearest listed number to that intermediate 46. Tested directly, a Laxmi of 45 would have been 41 four years ago, which is not twice Rahul's 23.

Concept: Age problems are systems of linear equations in disguise, and two structural facts make them routine. First, the difference between two people's ages never changes, because both age at the same rate; a relationship stated for one moment therefore constrains every other moment, and the constant difference is a free consistency check. Second, a phrase such as 'four years ago' shifts everybody in the sentence by the same amount — it must be applied to Rahul as well as to Laxmi, not only to the person being described, and forgetting the second shift is the single commonest error in the topic. A third habit converts most of these questions from algebra into arithmetic: look for the statement that fixes one person absolutely, solve that one first, and let it propagate. Here 'in four year's time, Rahul will be 31' does exactly that, which is why the system never has to be solved simultaneously. It also helps to know which relations are proportional and which are additive. 'Three times as old as' is a ratio and does not survive the passage of time — Rahul was not three times Seema four years ago and will not be in four years — whereas the 23-year gap between Laxmi and Rahul survives every shift. Papers exploit that difference constantly by stating a ratio at one moment and asking about another.

State PCS 2025 Q8 — Science & Technology PYQ with Answer

State PCS 2025 Q8 — Science & Technology PYQ with Answer