RRB Technician Grade III 2024, 2025 PYQs

Concept: Take tank $=\text{LCM}(18,12,15)=180$ units; filling pipes add, emptying pipe subtracts.

1. B $=10$, C $=15$, A $=-12$ units/h
2. All three: $10+15-12=13$ units/h; in $5$ h $=65$ units
3. Remaining $=180-65=115$ units
4. B + C $=25$ units/h ⇒ time $=\frac{115}{25}=4.6$ h $=4$ h $36$ min

Trick: $0.6$ h $=0.6\times 60=36$ min.

Answer: (C) 4 hours 36 minutes

Concept: If $a,b,c,d$ are in proportion, $a:b=c:d$, i.e. $a\times d=b\times c$.

1. $7\times k=11\times 21$
2. $k=\frac{231}{7}$
3. $k=33$

Trick: $21$ is $3\times 7$, so $k=3\times 11=33$.

Answer: (C) 33

Concept: With two candidates and all votes valid, winner gets the rest; margin $=$ difference of percentages.

1. Loser $=40\%$, winner $=60\%$
2. Margin $=60\%-40\%=20\%$ of total $=1000$
3. Total $=\frac{1000\times 100}{20}=5000$

Trick: $20\%\to 1000$ ⇒ $100\%\to 5000$.

Answer: (B) 5000

Concept: Volume is conserved: number of marbles $=\frac{\text{volume of big sphere}}{\text{volume of one marble}}$.

1. $n=\frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}={\left(\frac{R}{r}\right)}^3$
2. $\frac{R}{r}=\frac{6}{0.2}=30$
3. $n={30}^3=27000$

Trick: For spheres, count $=(\text{radius ratio}{)}^3$ – $\frac{4}{3}\pi$ cancels.

Answer: (A) 27000

Concept: Average charge $=\frac{\text{total collection}}{\text{total visitors}}$; take visitors $2x,5x,13x$.

1. Collection $=2\times 15+5\times 7.5+13\times 2.5$
2. $=30+37.5+32.5=100$ (per $x$)
3. Visitors $=2+5+13=20$ (per $x$)
4. Average $=\frac{100}{20}=$ ₹5

Trick: Take $x=1$; the ratio factor cancels.

Answer: (A) ₹5

Concept: If $a:x::x:b$, then $x^2=a\times b$ (x is the mean proportional).

1. $x^2=3.2\times 16.2=51.84$
2. $x=\sqrt{51.84}=7.2$ (taking $x>0$)

Trick: $3.2\times 16.2=\frac{32\times 162}{100}=\frac{5184}{100}$ and $\sqrt{5184}=72$.

Answer: (B) 7.2

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

1. Here $a=75$, $b=25$
2. Expression $=(75+25{)}^2={100}^2$
3. $=10000$

Trick: Spot the pattern $a\times a+2\times a\times b+b\times b$ – no long multiplication needed.

Answer: (D) 10000

Concept: $\text{Average speed}=\frac{\text{total distance}}{\text{total time}}$.

1. Time 1 $=\frac{60}{40}=1.5$ h, time 2 $=\frac{120}{80}=1.5$ h
2. Total distance $=180$ km, total time $=3$ h
3. Average $=\frac{180}{3}=60$ km/h

Trick: Equal times ⇒ average speed $=\frac{40+80}{2}=60$ km/h.

Answer: (C) 60 km/h

Concept: Adding the same number to every observation increases the average by that number.

1. Old average $=7$
2. Each number $+21$ ⇒ average $+21$
3. New average $=7+21=28$

Yaad rakhein: Add/subtract $k$ to all → average changes by $k$; multiply all by $k$ → average $\times k$.

Answer: (C) 28

Concept: Diagonals of a rhombus bisect each other at ${90}^{\circ }$; area $=\frac{1}{2}{d}_1{d}_2$.

1. Side $=\frac{100}{4}=25$ cm; half of given diagonal $=20$ cm
2. Other half $=\sqrt{{25}^2-{20}^2}=\sqrt{225}=15$ ⇒ $d_2=30$ cm
3. Area $=\frac{1}{2}\times 40\times 30=600{\text{ cm}}^2$

Trick: $15,20,25$ is the triplet $3,4,5$ scaled by $5$.

Answer: (B) 600 ${\text{cm}}^2$

Concept: Half-diagonals and a side form a right triangle: $a=\sqrt{{\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2}$.

1. Half-diagonals $=5$ cm and $12$ cm
2. $a=\sqrt{5^2+{12}^2}=\sqrt{169}$
3. $a=13$ cm

Trick: $5,12,13$ is a Pythagorean triplet.

Answer: (A) 13 cm

Concept: The expression has the form $a^2-2ab+b^2=(a-b{)}^2$.

1. Here $a=75$, $b=25$.
2. Value $=(75-25{)}^2={50}^2$.
3. ${50}^2=2500$.

Trick: Spot the middle term $-2\times 75\times 25$ — it signals $(a-b{)}^2$, no need to multiply each term.

Answer: (D) 2500

Concept: Work done = rate $\times$ time; take the tank as 1 (or LCM of 15 and 20 $=60$ units).

1. Tank $=60$ units; A fills $4$ units/min, B fills $3$ units/min.
2. In 4 min together: $4\times (4+3)=28$ units.
3. Remaining $60-28=32$ units by B alone: $\frac{32}{3}=10\frac{2}{3}$ min $=10$ min 40 s.
4. Total $=4+10\frac{2}{3}=14\frac{2}{3}$ min $=14$ min 40 s.

Trick: LCM-unit method avoids fractions: $\frac{2}{3}$ min $=40$ s.

Answer: (C) 14 min 40 sec

Concept: To cross a bridge, a train covers (its length + bridge length).

1. Distance $=100+150=250$ m.
2. Speed $=36\times \frac{5}{18}=10$ m/s.
3. Time $=\frac{250}{10}=25$ s.

Yaad rakhein: km/h to m/s: multiply by $\frac{5}{18}$ (36 km/h $=10$ m/s).

Answer: (B) 25

Concept: Area $=\pi r^2$, so area changes with the square of the radius.

1. New radius $=\frac{r}{2}$.
2. New area $=\pi {\left(\frac{r}{2}\right)}^2=\frac{1}{4}\pi r^2$.
3. Reduction $=1-\frac{1}{4}=\frac{3}{4}=75\%$.

Trick: Net % change $=a+b+\frac{ab}{100}=-50-50+\frac{2500}{100}=-75\%$.

Answer: (C) 75%

Concept: For a pure recurring part: $0.\overline{ab}=\frac{ab}{99}$.

1. $1.\overline{24}=1+\frac{24}{99}$.
2. $=\frac{99+24}{99}=\frac{123}{99}$.
3. Divide by 3: $\frac{41}{33}$.

Trick: Always reduce — $\frac{124}{99}$ and $\frac{123}{90}$ are traps for wrong rules.

Answer: (D) $\frac{41}{33}$

Concept: Mean proportional of $a$ and $b$ $=\sqrt{ab}$.

1. $ab=0.06\times 24=1.44$.
2. $\sqrt{1.44}=1.2$.

Trick: $\sqrt{1.44}=1.2$ because ${12}^2=144$ (two decimal places in 1.44 → one in the root).

Answer: (D) 1.2

Concept: Exterior angle at a vertex $={180}^{\circ }-$ interior angle $=$ sum of the two opposite interior angles.

1. $\angle C={180}^{\circ }-{70}^{\circ }-{70}^{\circ }={40}^{\circ }$.
2. Exterior $\angle A={180}^{\circ }-{70}^{\circ }={110}^{\circ }$.
3. Check: $\angle B+\angle C={70}^{\circ }+{40}^{\circ }={110}^{\circ }$.

Yaad rakhein: Interior and exterior angles at the same vertex form a linear pair (${180}^{\circ }$).

Answer: (A) ${110}^{\circ }$

Concept: Volume is conserved on recasting: $\frac{4}{3}\pi R^3=27\times \frac{4}{3}\pi r^3$; surface area $=4\pi r^2$.

1. ${12}^3=27r^3\Rightarrow r^3=64\Rightarrow r=4$ cm.
2. Original area $=4\pi (12{)}^2=576\pi$.
3. 8 small spheres: $8\times 4\pi (4{)}^2=512\pi$.
4. Ratio $=576:512=9:8$.

Trick: $27=3^3$ spheres → each radius $=\frac{R}{3}$; ratio $=R^2:8r^2=144:128$.

Answer: (B) 9 : 8

Concept: Square root of a decimal has half as many decimal places.

1. $0.0009=\frac{9}{10000}$.
2. $\sqrt{0.0009}=\frac{3}{100}=0.03$.

Trick: Check by squaring: ${0.03}^2=0.0009$.

Answer: (A) 0.03