RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Make the common term (red) equal in both ratios.

1. Red : Green $=7:20$ and Pink : Red $=15:12$, i.e. Red : Pink $=12:15=4:5$.
2. LCM of red values $7$ and $4$ is $28$: R : G $=28:80$, R : P $=28:35$.
3. Green : Pink $=80:35=16:7$.

Trick: $\frac{G}{P}=\frac{G}{R}\times \frac{R}{P}=\frac{20}{7}\times \frac{12}{15}=\frac{16}{7}$.

Answer: (C) $16:7$

Concept: Profit is shared in the ratio of investments (same time).

1. Profit left after charity $=69\%$ of $76700=52923$.
2. Ratio $56000:52000:69000=56:52:69$; total $=177$ parts.
3. One part $=\frac{52923}{177}=299$.
4. Suresh $=69\times 299=20631$.

Trick: Check divisibility early: $52923÷177=299$ exactly confirms the setup.

Answer: (A) ₹$20,631$

Concept: Range = highest value − lowest value.

1. Highest mark $=80$, lowest mark $=45$.
2. Range $=80-45=35$.

Trick: Only the two extremes matter for range — ignore the middle values.

Answer: (D) $35$

Concept: Volume of cone $V=\frac{1}{3}\pi r^{2}h$; water $=\frac{2}{3}$ of $V$.

1. $V=\frac{1}{3}\pi \times {31}^2\times 45=15\times 961\pi =14415\pi {\text{cm}}^3$.
2. Water $=\frac{2}{3}\times 14415\pi =9610\pi {\text{cm}}^3$.

Trick: Combine fractions: $\frac{2}{3}\times \frac{1}{3}\times 45=10$, so answer $=10\times 961\pi$.

Answer: (C) $9610\pi$

Concept: $\text{CP}=\frac{\text{SP}}{1+\text{gain}}$.

1. SP of 1 chocolate $=\frac{1}{4}$ rupee.
2. Gain $100\%$ → CP $=\frac{1}{2}\times \frac{1}{4}=\frac{1}{8}$ rupee per chocolate.
3. So for ₹1 he bought $8$ chocolates.

Trick: 100% gain means CP is half of SP → he bought twice as many per rupee: $2\times 4=8$.

Answer: (C) $8$

Concept: Subtract the same $x$ years from both ages.

1. $x$ years ago: Arvind $=40-x$, Asha $=25-x$.
2. $40-x=4(25-x)\Rightarrow 40-x=100-4x$.
3. $3x=60\Rightarrow x=20$.

Trick: Check: 20 years ago ages were $20$ and $5$; $20=4\times 5$. ✓

Answer: (B) $20$ years

Concept: Average = sum ÷ number of values.

1. Sum $=20+30+35+40+45=170$.
2. Average $=\frac{170}{5}=34$ years.

Trick: Deviation from 35: $-15,-5,0,+5,+10$ → total $-5$ → $35-1=34$.

Answer: (A) $34$

Concept: Winning margin as a percentage of total votes.

1. Loser $=48\%$, winner $=52\%$ (only two candidates).
2. Margin $=52\%-48\%=4\%$ of total $=756$.
3. Total $=\frac{756\times 100}{4}=18900$.

Trick: Margin % $=100-2\times 48=4\%$; then $756\times 25$.

Answer: (D) $18900$

Concept: The perpendicular from the centre bisects the chord; use Pythagoras.

1. Half chord $AM=\frac{12}{2}=6\text{cm}$, $OM=5\text{cm}$.
2. $r^2=6^2+5^2=36+25=61$.
3. $r=\sqrt{61}\approx 7.81\text{cm}$.

Trick: $\sqrt{61}$ lies between ${7.8}^2=60.84$ and ${7.9}^2=62.41$ → only 7.81 fits.

Answer: (A) $7.81\text{cm}$

Concept: Volume is conserved; surface area $=4\pi r^2$.

1. $\frac{4}{3}\pi (10{)}^3=125\times \frac{4}{3}\pi r^3\Rightarrow r^3=8\Rightarrow r=2\text{cm}$.
2. Big sphere SA $=4\pi (10{)}^2=400\pi$.
3. 6 small spheres SA $=6\times 4\pi (2{)}^2=96\pi$.
4. Ratio $=400:96=25:6$.

Trick: $n$ equal spheres → $r=\frac{R}{\sqrt[3]{n}}$; here $\frac{10}{5}=2$.

Answer: (B) $25:6$

Concept: Equation with sum $S$ and product $P$ of roots: $x^2-Sx+P=0$.

1. $S=4-3\sqrt{2}$, $P=-28$.
2. $x^2-(4-3\sqrt{2})x+(-28)=0$.
3. $x^2-(4-3\sqrt{2})x-28=0$.

Trick: Sign rule: minus sum, plus product — so a negative product appears as $-28$.

Answer: (D) $x^2-(4-3\sqrt{2})x-28=0$

Concept: $\text{CP}=\frac{\text{MP}}{1.25}$ when MP is 25% above CP; $\text{SP}=\text{MP}\times (1-\text{discount})$.

1. $\text{CP}=\frac{7725}{1.25}=6180$
2. $\text{SP}=7725\times 0.96=7416$
3. $\text{Profit}=7416-6180=1236$; $\frac{1236}{6180}\times 100=20\%$

Trick: Take CP = 100 → MP = 125 → SP = $125\times 0.96=120$ → profit $20\%$ directly.

Answer: (C) $20\%$

Concept: Gap between the two cabs stays fixed. The man (moving towards them) closes this gap at relative speed $(74+v)$.

1. Gap $=74\times \frac{28}{60}\text{km}$
2. Man covers it in 10 min: $(74+v)\times \frac{10}{60}=74\times \frac{28}{60}$
3. $740+10v=2072\Rightarrow v=133.2\text{km/h}$

Trick: $v=\frac{74(28-10)}{10}=\frac{74\times 18}{10}=133.2$.

Answer: (B) $133.2$

Concept: Monthly saving = income − expenses; in the birthday month the saving becomes zero.

1. Monthly saving $=10000-6000-2500=1500$
2. Savings occur in 11 months only.
3. Yearly savings $=1500\times 11=16500$

Trick: One month lost → multiply by 11, not 12.

Answer: (B) ₹16,500

Concept: Net filling rate = filling rate − emptying rate.

1. Net per minute $=\frac{1}{10}-\frac{1}{20}=\frac{1}{20}$
2. Time = 20 minutes.

Trick: Time $=\frac{ab}{b-a}=\frac{10\times 20}{20-10}=20$.

Answer: (D) 20

Concept: Make the common term (y) equal to combine the ratios.

1. $x:y=2:5=8:20$, $y:z=4:7=20:35$ → $x:y:z=8:20:35$
2. Total parts = 63; one part $=rac1512063=240$
3. $x=1920,y=4800,z=8400$

Trick: Multiply crosswise: $x:y:z=2\times 4:5\times 4:5\times 7$.

Answer: (D) 1,920, 4,800 and 8,400

Concept: If 40% is spent, 60% is saved.

1. $60\%$ of income $=18000$
2. Income $=\frac{18000\times 100}{60}=30000$

Trick: $1\%=300$ → $100\%=30000$.

Answer: (B) ₹30,000

Concept: Covered $=\frac{4}{3}$ × remaining → covered : remaining = 4 : 3.

1. Covered $=\frac{4}{7}\times 37=\frac{148}{7}\text{km}$
2. Time $=1\text{h}5\text{min}=\frac{13}{12}\text{h}$
3. Speed $=\frac{148}{7}\times \frac{12}{13}=\frac{1776}{91}\approx 19.5\text{km/h}$

Trick: "a is $\frac{p}{q}$ of b" → split total in $p:q$.

Answer: (B) $19.5$

Concept: $a:b::c:x$ means $\frac{a}{b}=\frac{c}{x}$, so $x=\frac{b\times c}{a}$.

1. $x=\frac{17.4\times 14}{3.5}$
2. $\frac{14}{3.5}=4$ → $x=17.4\times 4=69.6$

Trick: 14 is 4 times 3.5, so x is 4 times 17.4.

Answer: (C) $69.6$

Concept: Range $=y-x$; sum of marks $=\text{mean}\times n$.

1. Sum $=64\times 12=768$; known 10 marks add to $648$ → $x+y=120$
2. $y-x=70$
3. $x=25,y=95$ (25 below 28 and 95 above 83 ✓)

Trick: Sum and difference of x, y → add and halve.

Answer: (C) $(25,95)$