RRB Technician Grade III 2024, 2025 PYQs

Concept: Find CP and SP per kg; quantity = total profit ÷ profit per kg.

Solution:

1. CP = $15÷3=$ ₹5 per kg
2. SP = $50÷5=$ ₹10 per kg
3. Profit = ₹5 per kg → $125÷5=25$ kg

Trick: Always convert both rates to 'per kg' first — then it is one division.

Answer: (A) 25

Concept: Sum = average × count.

Solution:

1. Sum of 3 numbers = $20\times 3=60$
2. Third = $60-(11+21)=28$

Trick: Deviation method: 11 is −9, 21 is +1 from 20; third must be +8 → 28.

Answer: (C) 28

Concept: Write present ages as variables and translate each condition.

Solution:

1. John now = J; $J=2(J-10)\to J=20$
2. 5 years ago: $(J-5)+(S-5)=25\to J+S=35$
3. Jane $S=35-20=15$
4. Difference = $20-15=5$

Trick: 'Now twice of 10 years ago' always means present age = $2\times 10=20$.

Answer: (A) 5

Concept: In BODMAS, 'of' is done before ÷ and ×.

Solution:

1. Inside bracket: $\frac{1}{2}$ of $\frac{1}{2}=\frac{1}{4}$ first
2. $\frac{1}{2}÷\frac{1}{4}=2$; then $2+\frac{1}{2}=\frac{5}{2}$
3. $\frac{1}{2}$ of $\frac{5}{2}=\frac{5}{4}$
4. $\frac{5}{4}-\frac{1}{2}=\frac{3}{4}=0.75$

Trick: Common mistake: doing $\frac{1}{2}÷\frac{1}{2}$ first gives 1 — always solve 'of' before '÷'.

Answer: (A) 0.75

Concept: Net change = $a+b+\frac{ab}{100}$ (use − for decrease).

Solution:

1. $a=+30,b=-35$
2. Net = $30-35+\frac{30\times (-35)}{100}$
3. $=-5-10.5=-15.5\%$

Trick: Multiplier method: $1.30\times 0.65=0.845$ → 15.5% decrease.

Answer: (C) 15.5% decrease

Concept: $(a+b{)}^2-(a-b{)}^2=4ab$.

Solution:

1. $a=2pq,b=11q$
2. $4ab=4\times 2pq\times 11q$
3. $=88p{q}^2$

Trick: Check with $p=q=1$: ${13}^2-(-9{)}^2=169-81=88$ → only $88p{q}^2$ fits the $q^2$ power.

Answer: (C) 88pq2

Concept: Exterior angle = 180° − interior angle.

Solution:

1. Exterior = ${180}^{\circ }-{156}^{\circ }={24}^{\circ }$
2. All exterior angles of a regular polygon are equal
3. Sum of 7 of them = $7\times {24}^{\circ }={168}^{\circ }$

Yaad rakhein: Number of sides = 360° ÷ exterior angle = $360÷24=15$.

Answer: (C) 168°

Concept: Take the lowest power 2ⁿ common and cancel.

Solution:

1. Numerator = 2ⁿ(2³ − 2) = 6 × 2ⁿ
2. Denominator = 2 × 2² × 2ⁿ = 8 × 2ⁿ
3. Value = $\frac{6}{8}=\frac{3}{4}$

Trick: Put n = 0: $\frac{8-2}{2\times 4}=\frac{6}{8}=\frac{3}{4}$.

Answer: (D) $\frac{3}{4}$

Concept: Distance = train length + bridge length; speed = distance ÷ time.

Solution:

1. Distance = $240+420=660$ m
2. Speed = $660÷22=30$ m/s
3. $30\times \frac{18}{5}=108$ km/h

Trick: m/s → km/h: multiply by 3.6 ($30\times 3.6=108$).

Answer: (D) 108 km/h

Concept: $P=\frac{\text{SI}\times 100}{R\times T}$.

Solution:

1. $P=\frac{700\times 100}{10\times 2}$
2. $=\frac{70000}{20}=$ ₹3500

Trick: 10% for 2 years = 20% of P = 700 → P = $700\times 5=3500$.

Answer: (C) 3500

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: Use ${\sin }^2\theta +{\cos }^2\theta =1$ to reduce the equation to one ratio.

1. $10{\cos }^2\theta +7{\sin }^2\theta =7({\sin }^2\theta +{\cos }^2\theta )+3{\cos }^2\theta =7+3{\cos }^2\theta$
2. So $7+3{\cos }^2\theta =7\Rightarrow {\cos }^2\theta =0\Rightarrow \theta ={90}^{\circ }$
3. $\sin \theta +\cos \theta =1+0=1$

Trick: Write the bigger coefficient as $7+3$: the extra $3{\cos }^2\theta$ must be 0.

Answer: (A) 1

Concept: Form the equation and solve backwards.

1. $\frac{x}{3}+37=51\Rightarrow \frac{x}{3}=14$
2. $x=14\times 3=42$
3. Sum of digits = $4+2=6$

Trick: Reverse the operations: $(51-37)\times 3=42$.

Answer: (D) 6

Concept: $\text{SI}=\frac{P\times R\times T}{100}$, with T in years (9 months $=\frac{9}{12}=\frac{3}{4}$ year).

1. $\text{SI}=28260\times 9\times \frac{3}{4}÷100$
2. $=28260\times \frac{6.75}{100}=28260\times 0.0675$
3. = ₹1907.55

Trick: 9% for $\frac{3}{4}$ year = 6.75%; 1% of 28260 = 282.6, so $6.75\times 282.6=1907.55$.

Answer: (C) ₹ 1907.55

Concept: Opposite directions: relative speed = sum; distance = sum of lengths. Bridge: distance = train + bridge.

1. Relative speed = $54+72=126$ km/h $=126\times \frac{5}{18}=35$ m/s
2. Sum of lengths = $35\times 30=1050$ m $\Rightarrow 3k+2k=1050\Rightarrow k=210$; train P = 630 m
3. Speed of P = $54\times \frac{5}{18}=15$ m/s; in 90 s it covers 1350 m
4. Bridge = $1350-630=720$ m

Trick: km/h → m/s: multiply by $\frac{5}{18}$ (54 → 15, 72 → 20).

Answer: (A) 720 meters

Concept: Profit is shared in the ratio of capital × time.

1. $X:Y=12000\times 12:18000\times 6=144000:108000=4:3$
2. X's share = $25200\times \frac{4}{7}=$ ₹14,400

Trick: Cancel thousands first: $12\times 12:18\times 6=144:108=4:3$.

Answer: (C) ₹14,400