RRB Technician Grade III 2024, 2025 PYQs

Concept: Opposite sides of a parallelogram are equal, so $\text{Perimeter}=2(a+b)$.

1. Let the adjacent sides be $2x$ and $3x$.
2. $2(2x+3x)=60\Rightarrow 10x=60\Rightarrow x=6$
3. Shorter side $=2x=12$ cm

Trick: Half perimeter $=30$ splits in $2:3$ → $\frac{2}{5}\times 30=12$.

Answer: (A) 12 cm

Concept: For equal time, profit is shared in the ratio of investments.

1. Ratio $=30000:24000=5:4$
2. Total parts $=9$
3. A's share $=\frac{5}{9}\times 13500=7500$

Trick: $13500÷9=1500$ per part; A gets $5\times 1500=7500$.

Answer: (A) ₹7,500

Concept: Sum of exterior angles of any polygon is ${360}^{\circ }$; for a regular $n$-gon each is $\frac{{360}^{\circ }}{n}$.

1. Octagon: $n=8$
2. Each exterior angle $=\frac{{360}^{\circ }}{8}={45}^{\circ }$

Yaad rakhein: Interior angle $={180}^{\circ }-{45}^{\circ }={135}^{\circ }$ — a handy check.

Answer: (C) 45°

Concept: For an odd count of consecutive integers, the average equals the middle number.

1. 13 numbers: the 7th (middle) $=36$
2. Smallest $=36-6=30$, largest $=36+6=42$
3. $2\times 30+42=102$

Trick: Middle ± (count − 1)/2 gives the ends instantly: $36\pm 6$.

Answer: (A) 102

Concept: Write the integer with the same denominator, then subtract numerators.

1. $\frac{-3}{13}-4=\frac{-3}{13}-\frac{52}{13}$
2. $=\frac{-3-52}{13}=\frac{-55}{13}$

Trick: $4=\frac{52}{13}$; just add $3+52$ and keep the minus sign.

Answer: (B) $\frac{-55}{13}$

Concept: Work done = rate × time; sum of fractions filled must equal 1.

1. A runs all 30 min: $\frac{30}{40}=\frac{3}{4}$ tank
2. B must fill $1-\frac{3}{4}=\frac{1}{4}$
3. B's time $=\frac{1}{4}\times 60=15$ min

Trick: Use LCM 120 units: A = 3/min, B = 2/min; A gives 90, B needs 30 → 15 min.

Answer: (A) 15 min

Concept: $\text{Sum}=\text{Average}\times \text{Number}$; the missing mark is the difference of the two sums.

1. Total of 7 subjects $=7\times 75=525$
2. Total of 6 subjects $=6\times 72=432$
3. Science $=525-432=93$

Trick: Science $=75+6\times (75-72)=75+18=93$.

Answer: (B) 93

Concept: If $x+y+z=0$, then $x^3+y^3+z^3=3xyz$.

1. Let $x=a-b,y=b-c,z=c-a$
2. $x+y+z=(a-b)+(b-c)+(c-a)=0$
3. So the sum $=3(a-b)(b-c)(c-a)$

Trick: Check with $a=2,b=1,c=0$: $1+1-8=-6$ and $3(1)(1)(-2)=-6$.

Answer: (C) $3(a-b)(b-c)(c-a)$

Concept: To compare roots of different orders, raise all to the power LCM of the indices.

1. LCM of 2, 3, 4 $=12$
2. $(\sqrt{2}{)}^{12}=2^6=64$, $(3^{1/3}{)}^{12}=3^4=81$, $(4^{1/4}{)}^{12}=4^3=64$
3. 81 is largest, so $3^{1/3}$ is greatest

Trick: Note $4^{1/4}=\sqrt{2}$ always, so those two can never be the unique greatest.

Answer: (C) $3^{1/3}$

Concept: Form an equation from the given difference of parts.

1. Let the number be $x$: $\frac{x}{3}-\frac{x}{5}=6$
2. $\frac{2x}{15}=6\Rightarrow x=45$
3. One-third $=\frac{45}{3}=15$

Trick: Take $x=15k$: $5k-3k=6\Rightarrow k=3$; one-third $=5k=15$.

Answer: (B) 15

Concept: Three (or more) parallel lines cut any two transversals in proportional intercepts.

1. First transversal: $AB:BC=3:5$
2. By the intercept theorem, $DE:EF=AB:BC$
3. So second transversal ratio $=3:5$

Yaad rakhein: Parallel lines keep the ratio unchanged; if they also cut equal parts on one, they cut equal parts on every transversal.

Answer: (A) 3 : 5

Concept: $\sqrt{1.0816}=\frac{\sqrt{10816}}{100}$ (4 decimal places → 2 in the root).

1. ${104}^2=10816$
2. $\sqrt{1.0816}=\frac{104}{100}=1.04$

Trick: Last digit 6 → root ends in 4 or 6; ${1.04}^2=1.0816$ checks instantly.

Answer: (D) 1.04

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

1. $R=\frac{520\times 100}{1300\times 8}$
2. $=\frac{52000}{10400}=5\%$

Trick: SI is $\frac{520}{1300}=40\%$ in 8 years → $\frac{40}{8}=5\%$ per year.

Answer: (D) 5%

Concept: If one piece is $\frac{2}{5}$ of the other, the pieces are in ratio $2:5$.

1. Total parts $=2+5=7$
2. Shorter piece $=\frac{2}{7}\times 70=20$ cm

Trick: $70÷7=10$ per part; shorter $=2\times 10=20$.

Answer: (D) 20 cm

Concept: Take the third number as 100 and express both numbers from it.

1. First $=100-30=70$, second $=100-37=63$
2. $\frac{63}{70}\times 100=90\%$

Trick: $\frac{63}{70}=\frac{9}{10}$ — just cancel 7.

Answer: (C) 90%

Concept: Order: Brackets → Division/Multiplication → Addition/Subtraction.

1. Bracket: $4\times 6=24$
2. Division: $48÷24=2$
3. $10+8+6-2=22$

Yaad rakhein: Always solve the bracket first, then the division.

Answer: (B) 22

Concept: ${\sin }^2\theta +{\cos }^2\theta =1$, ${\sec }^2\theta -{\tan }^2\theta =1$, $\tan \theta =\frac{\sin \theta }{\cos \theta }$.

1. ${\sin }^2\theta +{\cos }^2\theta -({\sec }^2\theta -{\tan }^2\theta )=1-1=0$
2. $\tan \theta \cos \theta =\frac{\sin \theta }{\cos \theta }\times \cos \theta =\sin \theta$
3. Total $=0+\sin \theta +\sin \theta =2\sin \theta$

Trick: Put $\theta ={30}^{\circ }$: $0+\frac{1}{2}+\frac{1}{2}=1=2\sin {30}^{\circ }$.

Answer: (B) $2\sin \theta$

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

1. $\text{SI}=\frac{200000\times 11\times 2}{100}$
2. $=2000\times 22=44000$

Trick: 11% of 2 lakh $=22000$ per year; 2 years → 44000.

Answer: (A) ₹44,000

Concept: $\text{SP}=\text{MP}\times (1-d_1)(1-d_2)$

1. After the 2nd discount: $x\times \frac{7}{8}=105\Rightarrow x=120$
2. First discount $=150-120=30$
3. $\frac{30}{150}\times 100=20\%$

Trick: $12.5\%=\frac{1}{8}$: price before it $=105\times \frac{8}{7}=120$.

Answer: (B) 20%

Concept: Do multiplication and division before addition and subtraction (left to right).

1. $5\times 3=15$ and $12÷4=3$
2. $15-3+8=20$

Yaad rakhein: Never subtract before dividing: $12÷4$ comes first.

Answer: (C) 20