‘M’ is 60 years old. ‘R’ is 5 years junior to ‘M’ and 4 years senior to ‘V’. The youngest brother of ‘V’ is ‘B’ and he is 6 years junior to ‘V’. What is the age difference between ‘M’ and ‘B’ ?
- (a)18 years
- (b)15 years
- (c)13 years
- (d)11 years
Answer
Why
Correct — B, (b) 15 years. Junior means younger, senior means older, and the chain then resolves in three steps. M is 60. R is 5 years junior to M, so R is 55. R is 4 years senior to V, so V is four years younger than R, which is 51. B is 6 years junior to V, so B is 45. The difference between M and B is 60 − 45 = 15 years. The more useful way to see it is that M's age of 60 never enters the answer at all. The question asks for a difference, and a difference along a chain of relatives is simply the sum of the gaps: 5 years from M to R, 4 from R to V, 6 from V to B, total 15. Had the stem said M was 70, or 34, the answer would still be 15 years — the 60 is there only to give the chain a starting point and to let you check each individual age as you go. 'The youngest brother of V' is decoration in the same way: it tells you B is younger than V, which the very next clause then states in numbers. One thing to register before you match 15 to a letter — the four options on this item are printed in DESCENDING order, 18, 15, 13, 11. That is the Commission's own arrangement, and the answer is the second option down, not the second from the bottom.
Why the others are wrong
- (a)18 years — 18 is larger than the whole chain, so it cannot be right whatever the arithmetic. The stem supplies exactly three gaps — 5 years, 4 years and 6 years — and every difference between any two of the four people named is built from them: 4, 5, 6, 9, 10, 11 and 15 are the complete list, and 15, the sum of all three, is the largest available. Any option above 15 has quietly invented a gap. This is the cheapest check on a question of this shape and it costs one line: add the gaps before you compute a single age, and use the total as a ceiling against which the options can be screened.
- (c)13 years — 13 is inside the ceiling but is still not reachable, because it is not the sum of any selection from 5, 4 and 6. Run the same inventory as for (a) — the only differences the stem can produce are 4, 5, 6, 9, 10, 11 and 15 — and 13 is disposed of without computing anybody's age. It is also worth seeing what 13 does not correspond to. Reversing a junior into a senior anywhere along the chain changes the total by twice that gap, so flipping the 4 gives 15 − 8 = 7, flipping the 5 gives 15 − 10 = 5, and flipping the 6 gives 15 − 12 = 3. A direction error therefore lands on 3, 5 or 7 — never on 13 — which is a reminder that this option corresponds to no coherent misreading at all.
- (d)11 years — 11 is 5 + 6, and it is the one wrong option here that a careful candidate can actually reach: it is what you get by attaching the last sentence to the wrong person. Read 'he is 6 years junior' as measured from R rather than from V and you get R = 55, B = 49 and a difference of 11, with the four-year R-to-V gap dropped out of the middle of the chain. The sentence invites it, because 'he' sits in a clause whose subject is B and whose nearest preceding name is B's own, and the six years have to be traced back past that to V. The defence is mechanical: before answering, draw the chain as one line — M, R, V, B — and write each gap on the link it belongs to. A mis-attached gap is then visible on the page instead of buried in a sentence.
Concept
The idea being tested is that an age difference is a fixed quantity, independent of when you measure it and independent of anybody's absolute age. If R is five years younger than M today, R was five years younger ten years ago and will be five years younger in twenty. So a question that asks only for a difference can be answered by adding the gaps along the chain and never computing an age at all. The second idea is direction, carried by two words that this paper uses in place of 'older' and 'younger'. Senior means earlier-born and therefore older; junior means later-born and therefore younger. A chain of such statements defines a total order — M oldest, then R, then V, then B — and the whole question is whether you can build that order from prose in one reading. Where a question mixes an absolute age with relative statements, the absolute age matters only if the question asks for an age; the moment it asks for a difference, the anchor becomes redundant information.
This is the last of the reasoning items on this page and it is a reading test wearing arithmetic's clothes. Every number in it is small, no operation is harder than subtraction, and the three ways to fail are all failures of attention: reversing a junior into a senior, hanging the last gap on the wrong person, or reading the descending option list as though it ascended. EPFO EO/AO papers label people with single capitals inside typographic quotation marks, which is deliberately abstract — there is no real-world plausibility to fall back on, so the ordering has to come entirely from the words. The habit that pays is to convert the prose into a single line of names with the gaps written between them before attempting the question that was actually asked.
Key facts
- Junior means younger; senior means older. The chain runs M (oldest), R, V, B (youngest).
- With M at 60: R is 55, V is 51 and B is 45, so the M-to-B difference is 15 years.
- The answer is the sum of the three gaps, 5 + 4 + 6 = 15, and does not depend on M's age of 60.
- The complete set of differences the stem can produce between any two of the four people is 4, 5, 6, 9, 10, 11 and 15.
- An age difference between two people never changes with time, which is why difference questions need no anchor.
- Reversing the direction of any one gap changes the total by twice that gap — landing on 3, 5 or 7 here.
- The four options on this item are printed in descending order: 18, 15, 13, 11.
Study next
Common traps
- Swapping junior and senior, which reverses one link and moves the answer to 3, 5 or 7.
- Attaching the final six years to R instead of to V, which loses the middle gap and yields 11.
- Computing all four ages when only a difference was asked for, which multiplies the chances of a slip.
- Assuming numeric options ascend from (a) to (d). On this item they run downwards: 18, 15, 13, 11.
- Treating 'the youngest brother of V' as information about other siblings whose ages must be worked out. It only fixes that B is younger than V.
EPFO EO/AO reasoning blocks reliably carry one comparison chain, usually about ages or about seats in a row, with the people named by single capital letters. The stem is two or three sentences long, the arithmetic never exceeds addition and subtraction, and the difficulty is placed entirely in the direction words and in which person a pronoun refers back to.
Related PYQs
EPFO_EOAO_2020_Q84Open & attempt →The English alphabet is reordered in the following manner : The first 6 letters are written in opposite order, the next 6 letters are written in opposite order and so on. At the end, ‘Y’ is interchanged with ‘Z’. Which one of the following is the fourth letter to the right of the 13^th letter ?
- (a) N
- (b) O
- (c) M
- (d) I
Answer(a) N
The next item in this block, and the same skill applied to positions instead of years: a rule is described in prose, the sequence has to be rebuilt from it, and the answer is a count of places measured in a stated direction. Both are lost far more often to a misread instruction than to a miscalculation.
Practice
- practice — not a real PYQ
‘P’ is 52 years old. ‘Q’ is 6 years junior to ‘P’ and 4 years senior to ‘R’. ‘S’ is 9 years junior to ‘R’. What is the age difference between ‘P’ and ‘S’ ?
- (a)13 years
- (b)15 years
- (c)19 years
- (d)21 years
Answer(c) 19 years
- practice — not a real PYQ
‘X’ is 12 years senior to ‘Y’, and ‘Y’ is 5 years junior to ‘Z’. By how many years is ‘X’ senior to ‘Z’ ?
- (a)5 years
- (b)7 years
- (c)12 years
- (d)17 years
Answer(b) 7 years