BPSC 71st CCE Prelims General Studies · Question 8 of 150

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.

• (a)10, 50 — 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)9, 52 — 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)9, 45 — 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.

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.

Draw three columns headed four years ago, now and in four years, and fill in every person in every column before writing a single equation; the marks in this topic are lost by mixing the three moments, not by the arithmetic, which here never goes beyond a division by 3 and a doubling. Start with Rahul because his column is the only one fixed by a number, then read the other two sentences as instructions rather than as equations. The single discriminating computation is the last one: Laxmi's past age of 46 must be carried forward to 50. Everything else in the question is settled by then, and three of the four options already agree that Seema is 9. Two checks are worth distinguishing carefully. The age-gap check — Laxmi minus Rahul is 50 − 27 = 23 today and 46 − 23 = 23 four years ago — verifies that you shifted both people by the same four years, but it cannot by itself confirm the doubling, because any pair of ages keeps a constant gap. The relation check is what confirms the value: 46 must be exactly twice 23. Hindi-medium candidates should note one wording point in the booklet's own Hindi, which renders the first sentence as 'Rahul's age is 3 गुणा अधिक than Seema's'. Read absolutely strictly, '3 times more' would mean four times as much, which would make Seema 27 ÷ 4 = 6.75 — not a whole number and not among the options — so the reading the paper intends is the English one, three times as old.

• Rahul will be 31 in four years, so his present age is 31 − 4 = 27; this is the only age fixed to a number and every other value in the question follows from it.
• Rahul = 3 × Seema, so Seema is 27 ÷ 3 = 9 — a figure shared by three of the four options, which means the first line of working eliminates only option (a).
• Four years ago Rahul was 27 − 4 = 23, so Laxmi was 2 × 23 = 46 at that time, and her present age is 46 + 4 = 50, giving option (d).
• Written out, Laxmi's present age is 2x − 4 where x is Rahul's present age, so a one-year error in Rahul produces a two-year error in Laxmi: 27 gives 50 and 28 gives 52.
• The Laxmi-to-Rahul gap is 23 years at every moment — 50 − 27 today and 46 − 23 four years ago — which checks that both people were shifted by the same four years, though the doubling itself must be verified separately as 46 = 2 × 23.
• The Commission's published solution takes x = 3y, z − 4 = 2(x − 4) and x + 4 = 31, a triangular system that is solved by substitution alone, with no elimination required.

• Applying 'four years ago' to Laxmi alone and forgetting to move Rahul back as well — the single commonest error in the whole topic
• Leaving Laxmi at her past age of 46 instead of bringing her forward to the present 50, which is what makes 45 look plausible
• Using Rahul's future age of 31 in the ratio with Seema instead of his present age of 27, which produces the 10 in option (a)
• Counting 'in four year's time' inclusively and taking Rahul as 28, a one-year slip that doubles into the two-year error behind option (b)
• Assuming a stated ratio holds at every moment — Rahul is three times Seema today but was not four years ago and will not be in four years

BPSC sets an age problem in most preliminary papers and asks it plainly, with whole-number answers, one fully determined anchor age, and options that differ in only one of the two requested values so that a candidate who solves half the question still has to solve the other half. The wording always mixes three moments — some years ago, now, and some years hence — and the mark is lost by mixing them up rather than by the arithmetic. UPSC has not set an age sum in the General Studies paper since mental ability moved to Prelims Paper-II in 2011, and that paper has been merely qualifying at 33 per cent since 2015; but the older General Studies papers set them repeatedly and set them harder, chaining four relatives or two separate calendar years so that a genuine simultaneous system had to be built before any number could be extracted.

• practice — not a real PYQ

  The present age of a father is three times that of his son. Five years ago the father was four times as old as his son was then. What is the son's present age?

  • (a)15 years
  • (b)10 years
  • (c)20 years
  • (d)12 years

  Answer(a) 15 years — with son s and father 3s, 3s − 5 = 4(s − 5) gives s = 15, and the check holds: five years ago the father was 40 and the son 10, and 40 is four times 10.

• practice — not a real PYQ

  The present ages of A and B are in the ratio 4 : 5. Six years from now the ratio of their ages will be 14 : 17. What is B's present age?

  • (a)40 years
  • (b)45 years
  • (c)36 years
  • (d)50 years

  Answer(b) 45 years — taking the ages as 4x and 5x, (4x + 6) : (5x + 6) = 14 : 17 gives 68x + 102 = 70x + 84, so x = 9, B is 45 and A is 36; the check 42 : 51 does reduce to 14 : 17. Option (c) 36 is A's age, not B's.