RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Correct total = wrong total − wrong value + correct value.

1. Wrong total $=10\times 55=550$
2. Correct total $=550-48+84=586$
3. Correct average $=\frac{586}{10}=58.6$

Trick: Change in average $=\frac{84-48}{10}=3.6$, so $55+3.6=58.6$.

Answer: (D) 58.6

Concept: Take total work = LCM of days; work backwards from the end.

1. Total work $=\text{LCM}(16,10)=80$ units; Ramesh $=5$, Suresh $=8$ units/day.
2. Last 4 days Suresh alone: $4\times 8=32$ units.
3. Remaining $80-32=48$ units done together at 13 units/day: $\frac{48}{13}$ days.
4. Total $=\frac{48}{13}+4=\frac{100}{13}=7\frac{9}{13}$ days.

Trick: "Leaves x days before completion" → subtract the other person's x-day work first.

Answer: (B) $7\frac{9}{13}$ days

Concept: Sum = average × count.

1. First two numbers: $2\times 77=154$
2. Remaining two $=655-154-101=400$
3. Average $=\frac{400}{2}=200$

Trick: Subtract known parts from the total, then divide by how many are left.

Answer: (C) 200

Concept: Exterior angle bisectors at B and C meet at the excentre P, and $\angle P={90}^{\circ }-\frac{\angle A}{2}$.

1. $\angle CBD={180}^{\circ }-B$, $\angle BCE={180}^{\circ }-C$; halves are ${90}^{\circ }-\frac{B}{2}$ and ${90}^{\circ }-\frac{C}{2}$.
2. In $△BPC$: $\angle P={180}^{\circ }-({90}^{\circ }-\frac{B}{2})-({90}^{\circ }-\frac{C}{2})=\frac{B+C}{2}={90}^{\circ }-\frac{A}{2}$
3. $\angle P={90}^{\circ }-{42}^{\circ }={48}^{\circ }$

Trick: Internal bisectors: ${90}^{\circ }+\frac{A}{2}$; external bisectors: ${90}^{\circ }-\frac{A}{2}$.

Answer: (C) ${48}^{\circ }$

Concept: For $n$ odd, median = ${\left(\frac{n+1}{2}\right)}^{\text{th}}$ value after arranging in order.

1. Ascending order: 24, 26, 38, 39, 43, 49, 60, 61, 62, 72, 95
2. $n=11$, so median is the $6^{\text{th}}$ value.
3. Median $=49$

Trick: Always sort first – the 6th number in the given (unsorted) list is not the median.

Answer: (D) 49

Concept: In $a:b::c:d$, product of extremes = product of means.

1. $7:14::8.7:x\Rightarrow x=\frac{14\times 8.7}{7}=17.4$
2. $5:35::7:y\Rightarrow y=\frac{35\times 7}{5}=49$
3. $x:y=17.4:49=174:490=87:245$

Trick: $x=2\times 8.7$ and $y=7\times 7$ – the ratios are just "double" and "seven times".

Answer: (C) $87:245$

Concept: Speed in still water $=\frac{\text{downstream}+\text{upstream}}{2}$

1. Upstream speed $=\frac{176}{16}=11\text{km/h}$
2. Downstream speed $=\frac{85}{5}=17\text{km/h}$
3. Boat speed $=\frac{17+11}{2}=14\text{km/h}$ (stream $=3\text{km/h}$)

Trick: Boat = average of the two speeds; stream = half their difference.

Answer: (C) $14\text{km/h}$

Concept: Successive gains multiply: selling price $=\text{CP}\times \frac{110}{100}\times \frac{115}{100}\times \frac{125}{100}$.

1. Combined factor $=1.10\times 1.15\times 1.25=1.58125$.
2. Cost of production $=\frac{31900}{1.58125}\approx 20173.91$, i.e. about ₹20,173.91, not a whole number of rupees in the options.
3. Check each option: $20000\times 1.58125=31625$, $23200\times 1.58125=36685$, $25000\times 1.58125=39531.25$, $22000\times 1.58125=34787.5$; none gives ₹31,900.
4. So no option is correct as printed.

Note: Multiply the option by the combined factor to check it quickly. In the exam, every candidate gets full marks (bonus) for such a question.

Answer: Bonus – no option is correct as printed; full marks to all.

Concept: $\text{CSA}=2\pi rh$, $\text{TSA}=2\pi r(h+r)$

1. $2\pi rh=\frac{1}{2}\times 2\pi r(h+r)$
2. $2h=h+r\Rightarrow r=h=12\text{cm}$
3. Diameter $=2r=24\text{cm}$

Trick: CSA = half of TSA means CSA = area of the two ends, i.e. $2\pi rh=2\pi r^2\Rightarrow h=r$.

Answer: (A) 24

Concept: BODMAS – solve innermost brackets first, then multiplication, then addition, then division.

1. $(5-7)=-2$
2. $9\times (-2)=-18$
3. $\{21-18\}=3$
4. $81÷3=27$

Trick: Watch the sign: the small bracket is negative, so the curly bracket becomes $21-18$.

Answer: (A) 27

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