RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Let CP $=x$. Compare the two selling prices.

1. Actual SP $=0.89x$ (11% loss).
2. New CP $=0.95x$; new SP $=1.20\times 0.95x=1.14x$.
3. Difference: $1.14x-0.89x=0.25x=739$
4. $x=739\times 4=2956$

Trick: Difference of % on the same base: $114\%-89\%=25\%$ of CP = ₹739 ⇒ CP $=4\times 739$.

Answer: (C) ₹2,956

Concept: Area of a parallelogram $=\text{base}\times \text{height}$.

1. Area $=(3x-5y+4)(x-5y)$
2. $=3x^2-15xy-5xy+25y^2+4x-20y$
3. $=3x^2+25y^2-20xy+4x-20y$

Trick: Check signs: $(-5y)(-5y)=+25y^2$ and $xy$ terms $-15xy-5xy=-20xy$ — only (A) has both.

Answer: (A) $(3x^2+25y^2-20xy+4x-20y){\text{m}}^2$

Concept: $h=\sqrt{l^2-r^2}$ and $V=\frac{1}{3}\pi r^{2}h$.

1. $h=\sqrt{{25}^2-7^2}=\sqrt{576}=24\text{cm}$
2. $V=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24$
3. $=22\times 7\times 8=1232{\text{cm}}^3$

Trick: 7–24–25 is a Pythagorean triplet, so $h=24$ instantly.

Answer: (C) 1232

Concept: Simplify the fractions and convert to a whole-number ratio using the LCM of denominators.

1. $\frac{5}{20}:\frac{8}{16}:\frac{8}{14}=\frac{1}{4}:\frac{1}{2}:\frac{4}{7}$
2. Multiply by 28: $7:14:16$
3. Largest − smallest $=16k-7k=9k=54\Rightarrow k=6$
4. Largest $=16\times 6=96$

Trick: Compare decimals to spot the order: $0.25,0.5,0.57$ — so $\frac{8}{14}$ is largest.

Answer: (D) 96

Concept: Upstream speed $=b-s$, downstream speed $=b+s$.

1. Upstream speed $=\frac{32.2}{76/60}\approx 25.42\text{km/h}$
2. $b:s=9:8\Rightarrow$ upstream $=1$ part, downstream $=17$ parts
3. Downstream $=17\times 25.42\approx 432.2\text{km/h}$
4. Time $=\frac{44.9}{25.42}+\frac{57.8}{432.2}\approx 1.77+0.13\approx 1.9\text{h}$

Trick: With $b:s=9:8$, downstream speed is $\frac{9+8}{9-8}=17$ times the upstream speed.

Answer: (A) 1.9

Concept: In a perfect square every prime factor has an even power.

1. $2527=7\times 361=7\times {19}^2$
2. 19 already has an even power; 7 has power 1.
3. Multiply by 7: $2527\times 7=17689={133}^2$

Trick: Try dividing by small primes: $2527÷7=361={19}^2$ — leftover prime is the answer.

Answer: (C) 7

Concept: Take total work = LCM(10, 14, 21) = 210 units. Efficiency: Robert 21, Chris 15, Jeremy 10 units/day.

1. Let the work take $T$ days. Robert works 5 days, Chris $(T-2)$ days, Jeremy $T$ days.
2. $21\times 5+15(T-2)+10T=210$
3. $105-30+25T=210\Rightarrow 25T=135$
4. $T=5.4$ days

Trick: Write “days worked × efficiency” for each person and equate to total work.

Answer: (D) 5.4

Concept: Rotating a right triangle about one leg gives a cone: that leg = height, other leg = radius, hypotenuse = slant height.

1. $h=60$, $r=45$, $l=75\text{cm}$ (check: ${45}^2+{60}^2={75}^2$).
2. CSA $=\pi rl=\pi \times 45\times 75$
3. $=3375\pi {\text{cm}}^2$

Trick: The side you rotate about is always the height; CSA needs only $r$ and $l$.

Answer: (B) $3375\pi$

Concept: $A=P(1+\frac{RT}{100})$ for simple interest.

1. Total SI rate $=12\times 3=36\%$
2. $P\times 1.36=8500\Rightarrow P=6250$
3. SI $=8500-6250=2250$

Trick: SI $=A\times \frac{36}{136}=8500\times \frac{9}{34}=2250$.

Answer: (C) ₹2,250

Concept: Half-yearly compounding: rate per period $=\frac{R}{2}\%$, periods $=2\times \text{years}$.

1. 1.5 years = 3 half-years.
2. $\frac{1728}{1000}={\left(\frac{12}{10}\right)}^3\Rightarrow$ rate per half-year $=20\%$
3. Annual rate $R=2\times 20=40\%$

Trick: $1728={12}^3$ and $1000={10}^3$ — spot the cubes.

Answer: (D) 40%

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