RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Crossing distance = sum of lengths; same direction → subtract speeds, opposite → add speeds.

1. Same direction: $58-27=31\text{km/h}=\frac{31\times 5}{18}\text{m/s}$; time $=7.5\times 60=450\text{s}$.
2. $L+238=\frac{155}{18}\times 450=3875\Rightarrow L=3637\text{m}$.
3. Opposite: $58+38=96\text{km/h}=\frac{80}{3}\text{m/s}$.
4. Time $=\frac{3637+123}{80/3}=\frac{3760\times 3}{80}=141\text{s}$.

Trick: $\frac{5}{18}$ converts km/h to m/s; $96\times \frac{5}{18}=\frac{80}{3}$.

Answer: (C) $141$

Concept: For a fixed distance, time is inversely proportional to speed.

1. Speed becomes $\frac{2}{3}$, so time becomes $\frac{3}{2}$ of the normal time $t$.
2. Extra time $=\frac{3}{2}t-t=\frac{t}{2}=46$ minutes.
3. $t=92$ minutes.

Trick: Speed fraction $\frac{a}{b}$ → delay $=t\times \frac{b-a}{a}$; here $t\times \frac{1}{2}=46$.

Answer: (A) $92$

Concept: Average = sum of observations ÷ number of observations.

1. Sum $=500+600+450+550+400=2500$.
2. Average $=\frac{2500}{5}=500$.

Trick: Take 500 as base: deviations $0+100-50+50-100=0$, so average is ₹500.

Answer: (A) ₹500

Concept: Take the third number as 100 and increase it by the given percentages.

1. First number $=100+47=147$.
2. Second number $=100+25=125$.
3. Ratio $=147:125$ (no common factor).

Trick: With base 100, "$x\%$ more" is simply $100+x$.

Answer: (D) $147:125$

Concept: Let the total time be $T$ days; Nirbhay works $T-4$ days and Vismay works all $T$ days.

1. $\frac{T-4}{19}+\frac{T}{6}=1$.
2. Multiply by 114: $6(T-4)+19T=114$.
3. $25T=138\Rightarrow T=\frac{138}{25}=5\frac{13}{25}$ days.

Trick: Check: Vismay alone does the last 4 days $=\frac{4}{6}$; rest $\frac{1}{3}$ by both at $\frac{25}{114}$ per day.

Answer: (A) $5\frac{13}{25}$ days

Concept: Average price = total cost ÷ total number of books.

1. Cost $=51\times 1120+49\times 900=57120+44100=101220$.
2. Books $=51+49=100$.
3. Average $=\frac{101220}{100}=1012.2$.

Trick: With 100 items, just shift the decimal of the total by two places.

Answer: (C) 1,012.2

Concept: Convert a ratio of fractions into whole numbers by multiplying with the LCM of the denominators.

1. LCM of 14, 14, 15 $=210$.
2. $\frac{4}{14}:\frac{7}{14}:\frac{16}{15}=60:105:224$.
3. Difference $=224-60=164$ parts $=41\Rightarrow 1$ part $=\frac{1}{4}$.
4. Largest $=\frac{224}{4}=56$.

Trick: $\frac{41}{164}=\frac{1}{4}$, so every part is a quarter.

Answer: (C) $56$

Concept: Form two equations in pen price $p$ and notebook price $n$.

1. $3p+12n=195\Rightarrow p+4n=65$.
2. $7n-4p=39$.
3. Put $p=65-4n$: $7n-260+16n=39\Rightarrow 23n=299\Rightarrow n=13$, $p=13$.
4. $12p+6n=156+78=234$.

Trick: Both prices equal ₹13, so $12p+6n=18\times 13=234$.

Answer: (C) ₹234

Concept: If savings are $20\%$, expenditure is $80\%$ of income.

1. $80\%$ of income $=960$.
2. Income $=\frac{960\times 100}{80}=1200$.

Trick: $\frac{960}{8}\times 10=1200$.

Answer: (C) 1,200

Concept: Solve innermost brackets first: ( ) → { } → [ ], with × before −.

1. $37-37\times 2=37-74=-37$.
2. $37-(-37)=74$.
3. $37-74=-37$.
4. $37-(-37)=74$.

Trick: Values alternate $-37,74,-37,74$ – four levels end at 74.

Answer: (D) 74

Concept: Equal amounts after different periods: $A(1.1{)}^{12}=B(1.1{)}^{13}$.

1. $A=1.1B\Rightarrow A:B=11:10$.
2. Total parts $=21\Rightarrow$ 1 part $=\frac{1617}{21}=77$.
3. Anil’s share $=11\times 77=847$.

Trick: Gap of 1 year at $10\%$ → shares in ratio $11:10$.

Answer: (A) ₹847

Concept: Ladder, wall and ground form a right triangle; the base is adjacent to the ${60}^{\circ }$ angle.

1. $\cos {60}^{\circ }=\frac{\text{base}}{\text{ladder}}$.
2. $\frac{1}{2}=\frac{4.5}{L}$.
3. $L=9\text{m}$.

Trick: At ${60}^{\circ }$ the hypotenuse is twice the adjacent side.

Answer: (D) $9\text{m}$

Concept: Grouped mode $=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$.

1. Mode 160 is the upper limit of 155-160; take $l=155,f_1=31,f_0=18,f_2=x,h=5$.
2. $160=155+\frac{31-18}{62-18-x}\times 5\Rightarrow \frac{65}{44-x}=5$.
3. $44-x=13\Rightarrow x=31$.

Trick: Mode lies exactly on the boundary 160 only when $f_1=f_2$, so $x=31$.

Answer: (B) 31

Concept: Cross-multiply: $\frac{X}{147}=\frac{48}{X}\Rightarrow X^2=147\times 48$.

1. $147\times 48=7056$.
2. $X=\sqrt{7056}=84$ (positive value).
3. Or: $147\times 48=(49\times 3)(16\times 3)=49\times 16\times 9\Rightarrow X=7\times 4\times 3=84$.

Trick: Split into perfect squares: $49\times 16\times 9$.

Answer: (A) 84

Concept: A biquadratic $x^4+b{x}^2+c=0$ becomes quadratic with $y=x^2$.

1. $y^2-13y+36=0$.
2. $(y-9)(y-4)=0\Rightarrow y=9$ or $y=4$.
3. (Then $x=\pm 3,\pm 2$.)

Trick: Find two numbers with sum 13 and product 36: 9 and 4.

Answer: (A) 9, 4

Concept: Perimeter of a sector $=2r+l$, where arc length $l=r\theta$ ($\theta$ in radians).

1. $r=10.5$, $\theta =\frac{2\pi }{3}$ (i.e. ${120}^{\circ }$).
2. $l=10.5\times \frac{2}{3}\times \frac{22}{7}=7\times \frac{22}{7}=22$
3. Perimeter $=2\times 10.5+22=21+22=43$ cm

Trick: $\frac{2\pi }{3}$ is one-third of the full circle: circumference $=2\times \frac{22}{7}\times 10.5=66$, so arc $=\frac{66}{3}=22$.

Answer: (B) $43$

Concept: Under simple interest the interest is the same every year, so the difference of two amounts gives the interest for the extra years.

1. Interest for 2 years $=3000-1750=1250$, so 1 year $=625$.
2. Principal $=1750-2\times 625=500$
3. Rate $=\frac{625}{500}\times 100=125\%$

Trick: Rate $=\frac{A_2-A_1}{A_1{t}_2-A_2{t}_1}\times 100=\frac{1250}{1750\times 4-3000\times 2}\times 100=\frac{1250}{1000}\times 100=125\%$

Answer: (A) $125\%$

Concept: After successive increases of $a\%$ and $b\%$, value $=x(1+\frac{a}{100})(1+\frac{b}{100})$.

1. $x\times 1.04\times 1.20=156000$
2. $x\times 1.248=156000$
3. $x=\frac{156000}{1.248}=125000$

Trick: Check options: $125000\times 1.04=130000$, $130000\times 1.2=156000$ ✓

Answer: (A) ₹1,25,000

Concept: Remainder theorem: when $p(x)$ is divided by $(x-k)$, the remainder is $p(k)$.

1. $p(2)=a(8)+4(4)+3(2)-4=8a+18$
2. $q(2)=8-14+a=a-6$
3. Equal remainders: $8a+18=a-6\Rightarrow 7a=-24$
4. $a=-\frac{24}{7}$

Trick: Just put $x=2$ in both and equate — no long division needed.

Answer: (B) $-\frac{24}{7}$

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

1. 300% more than 360 means $4\times 360={1440}^{\circ }$.
2. $(n-2)\times 180=1440\Rightarrow n-2=8\Rightarrow n=10$
3. Each interior angle $=\frac{1440}{10}={144}^{\circ }$

Trick: Interior : exterior sum $=4:1$ ⇒ each interior : exterior $=4:1$ ⇒ interior $=\frac{4}{5}\times 180={144}^{\circ }$.

Answer: (D) $144$