RRB Technician Grade III 2024, 2025 PYQs

Concept: Add one-day works; A = B + C means A's rate equals (B + C)'s rate.

Solution:

1. $A+B=\frac{1}{6},C=\frac{1}{42}\to A+B+C=\frac{7}{42}+\frac{1}{42}=\frac{8}{42}=\frac{4}{21}$
2. $A=B+C\to 2A=\frac{4}{21}\to A=\frac{2}{21}$
3. $B=\frac{1}{6}-\frac{2}{21}=\frac{7}{42}-\frac{4}{42}=\frac{3}{42}=\frac{1}{14}$
4. B alone = 14 days

Trick: LCM method: total work 42 units; A+B = 7, C = 1 → all = 8 → A = 4 → B = 3 → $42÷3=14$ days.

Answer: (B) 14

Concept: Replace ${\cos }^2\theta$ by $1-{\sin }^2\theta$ and solve the quadratic in $\sin \theta$.

Solution:

1. ${\sin }^2\theta -3\sin \theta +2=1-{\sin }^2\theta \to 2{\sin }^2\theta -3\sin \theta +1=0$
2. $(2\sin \theta -1)(\sin \theta -1)=0\to \sin \theta =\frac{1}{2}$ ($\sin \theta =1$ not allowed as $\theta <{90}^{\circ }$)
3. $\theta ={30}^{\circ }\to \frac{3}{2}\theta ={45}^{\circ },3\theta ={90}^{\circ }$
4. $\cot {45}^{\circ }+\sin {90}^{\circ }=1+1=2$

Trick: Try $\theta ={30}^{\circ }$ directly: $\sin =\frac{1}{2}$ gives $(\frac{1}{4}-\frac{3}{2}+2)=\frac{3}{4}={\cos }^2{30}^{\circ }$ ✓.

Answer: (C) 2

Concept: Co-prime pairs have HCF 1. Count all pairs, subtract pairs sharing a factor.

Solution:

1. Numbers 11 to 19 = 9 numbers → total pairs = 9C2 = 36
2. Common factor 2: {12, 14, 16, 18} → 4C2 = 6 pairs
3. Common factor 3: {12, 15, 18} → 3 pairs, but (12, 18) already counted → 2 more
4. Co-prime pairs = 36 − 6 − 2 = 28

Yaad rakhein: Any two consecutive numbers are always co-prime; 1 is co-prime to every number.

Answer: (C) 28

Concept: $a:b=c:x\to x=\frac{b\times c}{a}$.

Solution:

1. $x=\frac{18\times 27}{12}$
2. $=\frac{486}{12}=40.5$

Trick: a : b = 12 : 18 = 2 : 3, so $x=27\times \frac{3}{2}=40.5$.

Answer: (B) 40.5

Concept: Use LCM as total work; find work done together, then the rest by B.

Solution:

1. Total work = $\text{LCM}(16,24)=48$ units; A = 3, B = 2 units/day
2. 5 days together = $5\times 5=25$ units
3. Remaining = 23 units
4. B takes $23÷2=11.5$ days

Trick: LCM-units method avoids fractions completely.

Answer: (B) 11.5 days

Concept: Decode each symbol and build the chain from Z to N.

Solution:

1. Z o C → Z is father of C
2. C ≥ L → C is wife of L
3. L @ M → L is brother of M; M x N → M is daughter of N, so L is N's son
4. C = N's son's wife; Z = her father → Z is N's son's wife's father

Trick: Read the chain backwards from N: son (L) → wife (C) → father (Z).

Answer: (C) Son's wife's father

Concept: A word common to two sentences gets the code common to both.

Solution:

1. 'share' appears in both sentences
2. Codes common to 'tn dp bk' and 'ps tn hv' = tn
3. share = tn

Trick: Just find the repeated word and the repeated code — no need to decode the rest.

Answer: (C) tn

Concept: Find the letter shifts from the first group to the second.

Solution:

1. W → V (−1), R → P (−2), T → Q (−3)
2. G → F (−1), U → S (−2), A → X (−3)
3. NXR: N − 1 = M, X − 2 = V, R − 3 = O → MVO ✓

Trick: Check the last letter first (−3): only option D gives R → O.

Answer: (D) NXR : MVO

Concept: Trace the relation from Bheem through his wife.

Solution:

1. Vidhi is Bheem's wife
2. Harshita and Vidhi are sisters; Ganesh is father of Harshita → Vidhi's father
3. Suraj is Ganesh's brother → Vidhi's uncle
4. So Suraj = Bheem's wife's father's brother

Trick: Start from Bheem: wife (Vidhi) → father (Ganesh) → brother (Suraj).

Answer: (C) Wife's father's brother

Concept: Locate both letters, then count letters between them in the A–Z alphabet.

Solution:

1. 5th from left: L F Q T G → G
2. 3rd from right: H, N, K → K
3. Between G and K in alphabet: H, I, J → 3

Trick: Letters between two letters = difference of positions − 1: K(11) − G(7) − 1 = 3.

Answer: (B) Three

Concept: Find the position gaps in each cluster.

Solution:

1. EJH: 5 → 10 → 8 (+5, −2)
2. PUS: 16 → 21 → 19 (+5, −2); QVT: 17 → 22 → 20 (+5, −2)
3. UHG: 21 → 8 → 7 — does not follow

Trick: Second letter is 5 ahead of the first in three clusters; in UHG it is behind.

Answer: (A) UHG

Concept: Swap the signs as told, then apply BODMAS.

Solution:

1. After swap: $7\times 2-64÷8+8$
2. $=14-8+8$
3. $=14$

Trick: Rewrite the full expression first; don't swap mentally while calculating.

Answer: (B) 14

Concept: Replace letters by signs, then use BODMAS.

Solution:

1. $71+45\times 5-15÷5\times 6+13-74+69$
2. $45\times 5=225$; $15÷5\times 6=18$
3. $71+225-18+13-74+69=286$

Trick: Last-digit check: $1+5-8+3-4+9=6$ → answer ends in 6 → 286 or 246; then exact sum gives 286.

Answer: (A) 286

Concept: Check each vowel's left and right neighbours.

Solution:

1. Vowels: E (B _ X ✓), I (X _ O ✗), O (I _ R ✗), O (M _ T ✓)
2. Qualifying vowels: E and the last O
3. Count = 2

Trick: Only vowels need checking — scan for A, E, I, O, U and look at both sides.

Answer: (B) Two

Concept: Each letter shifts by the same amount.

Solution:

1. B → Z, Y → W, R → P: each −2
2. H → F, E → C, Z → X: each −2
3. SIV → QGT (each −2) ✓

Trick: Check only the first letter (−2): S → Q fits A; G → D, M → L fail.

Answer: (A) SIV : QGT

Concept: Fix B, place others counting to B's right.

Solution:

1. Counting rightwards from B: O is 2nd, M is 4th (3 people between)
2. N neighbours M and O → N is 3rd
3. Seats 1st and 5th left for L and C; L 2nd to left of C → C 1st, L 5th
4. From right of B: C, O, then N → 2 people between

Trick: With 6 seats, 'three between' always means directly opposite.

Answer: (B) Two

Concept: Vowel → next letter; consonant → previous letter.

Solution:

1. W A M B L E S → V B L A K F R
2. All seven new letters are different
3. Letters appearing exactly twice = 0

Trick: A → B and B → A swap with each other, so no repeat is created.

Answer: (C) Zero

Concept: Compare each letter of the first cluster with the second.

Solution:

1. PG → TK: +4, +4; SJ → WN: +4, +4
2. MD → QH: +4, +4
3. VL → YO: +3, +3 → odd

Trick: Check just the first letters: P→T, S→W, M→Q are +4; V→Y is +3.

Answer: (D) VL – YO

Concept: Decode and link W to T.

Solution:

1. W ¥ X → W is daughter of X; X ~ Y → X is father of Y
2. Y ≤ Z → Y is sister of Z; Z £ T → Z is son of T
3. So W, Y, Z are siblings and children of T (X and T are parents)
4. W is female → W is T's daughter

Trick: Siblings share parents: W is a sibling of Z, and Z is T's child.

Answer: (A) Daughter

Concept: Find the rule for letters and number separately.

Solution:

1. CK 34 → BL 68: C − 1, K + 1, 34 × 2
2. HP 42 → GQ 84: same
3. NV 23 → M, W, 46 → MW 46

Trick: Number doubles → only 46 options; first letter −1 → M → MW 46.

Answer: (D) MW 46