RRB Technician Grade III 2024, 2025 PYQs

Concept: Innermost brackets first, then ÷/× before +/−.

Solution:

1. $24÷6=4\to (120-4)\times 2=232$; $50÷5+6=16\to 232-16=216$.
2. $18+24-8=34$; $9÷3+5=8\to 34-8=26$.
3. Total = $216+26=242$.

Yaad rakhein: Inside each bracket solve ÷ first — in $24÷(4+2)$, compute $(4+2)$ first.

Answer: (B) 242

Concept: Fourth proportional of a, b, c = $\frac{bc}{a}$.

Solution:

1. $x=7.5\times \frac{6.3}{3.5}$.
2. $\frac{6.3}{3.5}=1.8$.
3. $x=7.5\times 1.8=13.5$.

Trick: Spot $\frac{6.3}{3.5}=\frac{9}{5}$ first, then $7.5\times \frac{9}{5}=13.5$.

Answer: (A) 13.5

Concept: $\text{CSA}=2\pi rh,V=\pi r^{2}h$, so $V=\frac{\text{CSA}\times r}{2}$.

Solution:

1. $r=\frac{775.8}{2\times 3.14\times 24}=\frac{775.8}{150.72}\approx 5.1473$ cm.
2. $V=\frac{775.8\times 5.1473}{2}$.
3. $V\approx 1996.63{\text{cm}}^3$.

Trick: $V=\frac{\text{CSA}\times r}{2}$ skips recomputing π and h.

Answer: (D) 1996.63 cm3

Concept: Savings % = 100 − total spending %.

Solution:

1. Spending = $25+20+15=60\%$.
2. Savings = 40% of 84,000 = ₹33,600.

Trick: 10% of 84,000 = 8,400 → $40\%=4\times 8,400=33,600$.

Answer: (C) 33,600

Concept: Opposite direction: relative speed = sum; distance = sum of lengths.

Solution:

1. Train speed = $\frac{200}{10}=20$ m/s.
2. Other train = $60\times \frac{5}{18}=\frac{50}{3}$ m/s; relative = $20+\frac{50}{3}=\frac{110}{3}$ m/s.
3. Distance = $200+350=550$ m.
4. Time = $550\times \frac{3}{110}=15$ s.

Trick: 20 m/s = 72 km/h; $72+60=132$ km/h $=\frac{110}{3}$ m/s → $550÷\frac{110}{3}=15$ s.

Answer: (A) 15 seconds

Concept: One-day work = $\frac{1}{\text{days}}$; work done = rate × time.

1. A's 1-day work $=\frac{1}{12}$, B's $=\frac{1}{6}$. Together = $\frac{1}{12}+\frac{2}{12}=\frac{3}{12}=\frac{1}{4}$ per day.
2. In 2 days: $2\times \frac{1}{4}=\frac{1}{2}$ work done. Remaining $=\frac{1}{2}$.
3. A alone: $\frac{1}{2}÷\frac{1}{12}=6$ days.

Trick: LCM method: total work = LCM(12, 6) = 12 units; A = 1, B = 2 units/day. 2 days → 6 units; left 6 units ÷ 1 = 6 days.

Answer: (D) 6

Concept: Gap between two scores in % = gap in marks (pass mark lies between them).

1. 91% score is 187 above pass mark; 36% score is 60.5 below pass mark.
2. So $(91\%-36\%)=55\%$ of max $=187+60.5=247.5$.
3. Max marks = $247.5\times \frac{100}{55}=450$.

Trick: Passed by + failed by = difference of % → just add the two marks and divide by the % gap.

Answer: (D) 450

Concept: Sum 5 years ago + $2\times 5$ = present sum; then use $\frac{\text{sum}-\text{difference}}{2}$ for the younger.

1. Present sum = $60+5+5=70$ years.
2. $\text{Ayushi}-\text{Nidhi}=14$.
3. Nidhi = $\frac{70-14}{2}=28$ years.

Trick: Younger = $\frac{\text{Sum}-\text{Difference}}{2}$; elder = $\frac{\text{Sum}+\text{Difference}}{2}$.

Answer: (A) 28

Concept: Mode = the value that occurs most often.

1. Count: 52 → 4 times; 50 → 3 times; 44, 45, 47, 53 → 2 times each; others once.
2. Highest frequency = 4 for 52.

Trick: Only count the option values: 50 (3), 52 (4), 47 (2), 44 (2) – done in seconds.

Answer: (B) 52

Concept: Same direction: relative speed = difference; distance = sum of lengths.

1. Relative speed = $72-36=36$ km/h $=36\times \frac{5}{18}=10$ m/s.
2. Distance in 27 s = $10\times 27=270$ m $=L+180$.
3. $L=270-180=90$ m.

Trick: km/h → m/s: multiply by $\frac{5}{18}$ (36 km/h = 10 m/s, 72 km/h = 20 m/s).

Answer: (B) 90 m

Concept: Mode = 3 Median − 2 Mean.

1. Mode = $3\times 51-2\times 19$
2. $=153-38=115$

Trick: Remember "3 Me − 2 M": median gets 3, mean gets 2.

Answer: (A) 115

Concept: Overall profit % = weighted sum of each part's profit % (equal cost per item).

1. Take 100 items of CP ₹1: 40 at +17% → +6.8.
2. Remaining 60; 25% of 60 = 15 at +22% → +3.3.
3. Rest 45 at −10% → −4.5.
4. Net = 6.8 + 3.3 − 4.5 = 5.6 on 100 → 5.6%.

Trick: Take total = 100 so each part's share × its % gives the answer directly.

Answer: (D) 5.6%

Concept: Profit ratio = capital × time.

1. Kirti: $35,000\times 12$; Vaishnavi: $V\times 9$.
2. $35,000\times 12:9V=7:6$
3. $9V=4,20,000\times \frac{6}{7}=3,60,000\to V=$ ₹40,000.

Trick: Check options: $40,000\times 9=3,60,000$ and 4,20,000 : 3,60,000 = 7 : 6 ✓.

Answer: (B) ₹40,000

Concept: ${\sec }^2\theta -1={\tan }^2\theta$.

1. ${\sec }^2{60}^{\circ }-1={\tan }^2{60}^{\circ }$
2. $=(\sqrt{3}{)}^2=3$

Trick: Directly: $\sec {60}^{\circ }=2\to 4-1=3$.

Answer: (D) 3

Concept: Same base ⇒ equate powers; $\sqrt{27}=3^{3/2}$.

1. $2a-b=\frac{3}{2}$ and $a+b=\frac{3}{2}$.
2. Add: $3a=3\to a=1$.
3. $b=\frac{3}{2}-1=\frac{1}{2}$.

Trick: Subtracting the two equations gives $a-2b=0\to a=2b$; then $3b=\frac{3}{2}\to b=\frac{1}{2}$.

Answer: (B) $\frac{1}{2}$

Concept: $a:b=c:d\Rightarrow a\times d=b\times c$.

1. $8\times x=12\times 20$
2. $x=\frac{240}{8}=30$

Trick: 8 → 20 is ×2.5, so $12\times 2.5=30$.

Answer: (C) 30

Concept: A number is divisible by 4 if its last two digits are divisible by 4.

1. Last two digits = A4.
2. A = 0 → 04 = 4, divisible by 4 ✓ (also 24, 44, 64, 84).
3. Least value = 0.

Trick: Check the smallest option first – 04 works, stop.

Answer: (A) 0

Concept: Add/subtract whole parts and fraction parts separately.

1. Whole parts: $2+1-1=2$.
2. Fractions: $\frac{1}{2}+\frac{3}{4}-\frac{1}{4}=\frac{1}{2}+\frac{1}{2}=1$.
3. Total = $2+1=3$.

Trick: In decimals: $2.5+1.75-1.25=3$.

Answer: (C) 3

Concept: x as % of y = $(\frac{x}{y})\times 100$; maximum marks are irrelevant.

1. $\frac{B}{A}=\frac{50}{80}$
2. $=\frac{5}{8}\times 100=62.5\%$

Trick: $\frac{5}{8}=0.625\to 62.5\%$ (remember $\frac{1}{8}=12.5\%$).

Answer: (A) 62.5%

Concept: Quarterly: rate = $\frac{R}{4}$ per quarter, n = number of quarters.

1. Rate = $\frac{12}{4}=3\%$ per quarter; 6 months = 2 quarters.
2. $A=24,000\times (1.03{)}^2=24,000\times 1.0609$
3. = ₹25,461.60

Trick: Effective rate for 2 periods at 3% = $3+3+\frac{3\times 3}{100}=6.09\%$ → $24,000\times 6.09\%=1,461.60$.

Answer: (A) ₹25,461.60