RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Successive discounts multiply: net price factor $=\prod (1-d)$.

1. Factor $=0.80\times 0.87\times 0.80$
2. $=0.696\times 0.80=0.5568$
3. Single discount $=1-0.5568=0.4432=44.32\%$

Trick: Two at a time: $20+20-\frac{20\times 20}{100}=36\%$; then $36+13-\frac{36\times 13}{100}=44.32\%$.

Answer: (D) $44.32\%$

Concept: Cross-multiply a proportion: $\frac{X}{176}=\frac{99}{X}\Rightarrow X^2=176\times 99$.

1. $X^2=176\times 99=17424$
2. $176\times 99=16\times 11\times 9\times 11=(4\times 3\times 11{)}^2$
3. $X=4\times 3\times 11=132$

Trick: Factor first: $16\times 9\times {11}^2$ is a perfect square → $X=132$.

Answer: (A) 132

Concept: Grouped median $=l+\frac{\frac{N}{2}-cf}{f}\times h$.

1. $N=23+13+24+25+35=120$, $\frac{N}{2}=60$
2. Cumulative frequencies: 23, 36, 60, 85, 120 → median class 240–290
3. $l=240,cf=36,f=24,h=50$
4. Median $=240+\frac{60-36}{24}\times 50=240+50=290$

Trick: When $\frac{N}{2}$ equals a cumulative frequency exactly, the median is that class's upper limit (here 290).

Answer: (C) 290

Concept: $a:b::b:c\Rightarrow b^2=ac$.

1. $b^2=a\times 25a=25a^2\Rightarrow b=5a$
2. $20=5a\Rightarrow a=4$
3. $c=25a=100$

Trick: Check: $4:20=20:100$ (both $=\frac{1}{5}$).

Answer: (C) 100

Concept: Multiply numerator and denominator by $\cos \theta$: $\sec \theta \to 1$, $\tan \theta \to \sin \theta$.

1. $\frac{1-\sin \theta }{1+\sin \theta }=\frac{3}{5}$
2. $5-5\sin \theta =3+3\sin \theta \Rightarrow 8\sin \theta =2$
3. $\sin \theta =\frac{1}{4}\Rightarrow 2\sin \theta =\frac{1}{2}$

Trick: Componendo-dividendo: $\sin \theta =\frac{5-3}{5+3}=\frac{1}{4}$.

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

Concept: Under SI, interest per year is constant, so the difference of amounts gives interest for the extra years.

1. Interest for 2 years $=2000-1250=750$ → ₹375 per year
2. Principal $=1250-750=500$
3. Rate $=\frac{375}{500}\times 100=75\%$

Trick: $R=\frac{A_2-A_1}{A_1·t_2-A_2·t_1}\times 100=\frac{750}{1250\times 4-2000\times 2}\times 100=75\%$.

Answer: (B) $75\%$

Concept: Sum of exterior angles of any polygon $={360}^{\circ }$; sum of interior angles $=(n-2)\times {180}^{\circ }$.

1. Interior sum $=1.5\times {360}^{\circ }={540}^{\circ }$
2. $(n-2)\times 180=540\Rightarrow n=5$
3. Each interior angle $=\frac{{540}^{\circ }}{5}={108}^{\circ }$

Trick: Interior sum : exterior sum $=(n-2):2$ → $1.5=\frac{n-2}{2}\Rightarrow n=5$.

Answer: (D) 108

Concept: Weighted average $=\sum (\text{price}\times \text{weight})$ with weights as fractions.

1. $0.55\times 156=85.8$
2. $0.45\times 220=99$
3. Weighted average $=85.8+99=184.8$

Trick: $156+0.45\times (220-156)=156+28.8=184.8$.

Answer: (B) ₹184.80

Concept: Successive % growth works like compound interest: $P{(1+\frac{r}{100})}^n$.

1. Factor $={1.95}^2=3.8025$
2. Population 1950 $=348000\times 3.8025$
3. $=1323270$ → 13,23,270

Trick: Last digits: $348000\times 3.8025$ ends in …270 since $3.8025\times 1000=3802.5$ and $348\times 3802.5=1323270$.

Answer: (B) 13,23,270

Concept: Profit share ∝ capital × time (sum over each period).

1. Take capitals 30, 40, 100. X: $30\times 12=360$
2. Y: $40\times 6+20\times 6=360$
3. Z withdraws 40% after 3 months: $100\times 3+60\times 9=840$
4. Ratio $360:360:840=3:3:7$; Z $=\frac{7}{13}\times 23400=12600$

Trick: '9 months prior to completion' = after 3 months.

Answer: (A) 12,600

Concept: Solid hemisphere TSA = curved $2\pi r^2$ + flat base $\pi r^2=3\pi r^2$.

1. $r=16\text{cm}$, $r^2=256$
2. TSA $=3\pi \times 256=768\pi {\text{cm}}^2$

Trick: Solid hemisphere → $3\pi r^2$; hollow (curved only) → $2\pi r^2$.

Answer: (D) $768\pi {\text{cm}}^2$

Concept: Take total work = LCM(3, 9, 27) = 27 units; efficiencies 9, 3, 1 units/day.

1. Let total days $=n$. Nick works 1 day → 9 units.
2. Kevin works $n-2$ days → $3(n-2)$; Joe works $n$ days → $n$.
3. $9+3(n-2)+n=27\Rightarrow 4n=24\Rightarrow n=6$

Trick: All three for $n$ days $=13n$; subtract absences: $13n-9(n-1)-3\times 2=27\Rightarrow n=6$.

Answer: (D) 6

Concept: Mode = the value that occurs most often.

1. Counts: 4 → 5 times, 5 → 4 times, 7 → 3 times, 8 → 2 times; 2 and 9 once.
2. Highest frequency is for 4.

Trick: Tally quickly – mark each value once as you pass.

Answer: (D) 4

Concept: Write the numbers as $2k,7k,13k$; since 2, 7, 13 are pairwise co-prime, LCM $=2\times 7\times 13\times k$.

1. LCM $=182k=3094$
2. $k=\frac{3094}{182}=17$
3. HCF $=k=17$

Trick: Co-prime ratio terms → HCF = the common multiplier $k$.

Answer: (A) 17

Concept: Let one item cost $x$; the other costs $4800-x$. Write the total selling price as an equation.

1. $1.34x+0.90(4800-x)=5442$
2. $0.44x+4320=5442\Rightarrow 0.44x=1122\Rightarrow x=2550$
3. Other item $=4800-2550=2250$
4. Difference $=2550-2250=300$

Trick: If all were sold at 10% loss, SP would be ₹4320. Extra ₹1122 comes from $34\%+10\%=44\%$ of item 1, so item 1 $=\frac{1122}{0.44}=2550$.

Answer: (B) ₹300

Concept: Half-yearly compounding: rate per half-year $=\frac{1.1}{2}=0.55\%$. The January deposit earns for 2 half-years, the July deposit for 1 half-year.

1. Jan deposit: $7745[(1.0055{)}^2-1]=7745\times 0.01103025=85.43$
2. July deposit: $7745\times 0.0055=42.60$
3. Total interest $=85.43+42.60=128.03$

Trick: CI for 2 periods at $r\%$ $=2r+\frac{r^2}{100}=1.1+0.003025=1.103025\%$; add $0.55\%$ for the second deposit: $1.653025\%$ of 7745 $\approx 128.03$.

Answer: (B) ₹128.03

Concept: Divide each option by 41 and check the remainder.

1. $9430÷41=230$ exactly, since $41\times 230=9430$
2. $9879=41\times 240+39$; $9249=41\times 225+24$; $10113=41\times 246+27$ – not divisible

Trick: $9430=943\times 10$ and $943=41\times 23$ (since $41\times 23=943$).

Answer: (A) 9430

Concept: Use $(x-y{)}^2=(x+y{)}^2-4xy$.

1. $(x-y{)}^2={15}^2-4\times 36=225-144=81$
2. $x-y=\sqrt{81}=9$ (positive since $x>y$)
3. Check: $x=12,y=3$ ⇒ $12+3=15,12\times 3=36$

Trick: Find two numbers with product 36 and sum 15 directly: 12 and 3.

Answer: (B) 9

Concept: Crossing distance = sum of lengths; use relative speed (difference for same direction, sum for opposite).

1. Same direction: $78-62=16\text{km/h}=\frac{40}{9}\text{m/s}$; time $=4.5\times 60=270\text{s}$
2. $L_P+120=\frac{40}{9}\times 270=1200\Rightarrow L_P=1080\text{m}$
3. Opposite: $78+81=159\text{km/h}=159\times \frac{5}{18}=\frac{265}{6}\text{m/s}$
4. Time $=\frac{1080+245}{265/6}=\frac{1325\times 6}{265}=30\text{s}$

Trick: $1325=5\times 265$, so time $=5\times 6=30$ s.

Answer: (C) 30

Concept: Average $=\frac{\text{sum}}{\text{count}}$.

1. Sum $=8+12+10+14+6=50$
2. Average $=\frac{50}{5}=10$

Trick: Pair the deviations around 10: $-2,+2,0,+4,-4$ cancel out, so the average is 10.

Answer: (D) 10