RRB NTPC Undergraduate CBT 1 2024 PYQs

Concept: Mode is the value that occurs most often.

1. Frequencies: 19 → 3 times, 11 → 2 times, others once.
2. Highest frequency is for 19.

Trick: Just count repeats – no calculation needed.

Answer: (A) 19

Concept: Take CP $=x$; apply the markup and the discount one after the other.

1. $\text{LP}=1.5x$
2. $\text{SP}=1.5x\times 0.7=1.05x$, so profit $=0.05x$
3. $0.05x=91\Rightarrow x=1820$
4. $\text{LP}=1.5\times 1820=2730$

Trick: Net effect of +50% and −30%: $50-30-\frac{50\times 30}{100}=5\%$ profit.

Answer: (C) 2,730

Concept: Check each divisor with its divisibility rule.

1. Last digit is 5 (odd) → not divisible by 2; divisible by 5 ✔
2. Digit sum $=2+4+5+0+1+5=17$ → not divisible by 3, hence not by 15
3. For 11: $(5+0+4)-(1+5+2)=1$ → not divisible by 11

Yaad rakhein: A number ending in 0 or 5 is always divisible by 5.

Answer: (D) 5

Concept: Third proportional of $a$ and $b$ is $x$ where $a:b=b:x$, i.e. $x=\frac{b^2}{a}$.

1. $x=\frac{{51}^2}{9}$
2. $=\frac{2601}{9}=289$

Trick: $\frac{51}{9}=\frac{17}{3}$, so $x=51\times \frac{17}{3}=17\times 17=289$.

Answer: (D) 289

Concept: Successive discounts multiply: $\text{SP}=\text{MP}\times \frac{100-d_1}{100}\times \frac{100-d_2}{100}$.

1. $4500\times 0.75=3375$
2. $3375\times 0.8=2700$

Trick: 25% and 20% together $=25+20-\frac{25\times 20}{100}=40\%$ off: $0.6\times 4500=2700$.

Answer: (A) 2,700

Concept: Compare cost and selling price of one pen: $\text{Profit}\%=\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100$.

1. CP of one pen $=\frac{150}{12}=12.5$
2. SP $=44$, profit $=31.5$
3. $\text{Profit}\%=\frac{31.5}{12.5}\times 100=252\%$

Trick: Compare per dozen: SP $=44\times 12=528$ vs CP 150 → profit 378, $\frac{378}{150}\times 100=252$.

Answer: (D) 252

Concept: Surface area of a sphere $=4\pi r^2$.

1. $4\times 3.14\times 6^2$
2. $=12.56\times 36=452.16{\text{cm}}^2$

Trick: $4\pi r^2=4\times 113.04$: area of one great circle ($\pi r^2=113.04$) taken four times.

Answer: (C) 452.16 ${\text{cm}}^2$

Concept: Literate females = total literates − literate males.

1. Total literates $=0.78\times 374000=291720$
2. Literate males $=0.72\times 170000=122400$
3. Females $=204000$; literate females $=169320$
4. $\frac{169320}{204000}\times 100=83\%$

Trick: Alligation: males 170 and females 204 (ratio 5 : 6) mix to 78%; $\frac{78-72}{f-78}=\frac{6}{5}\Rightarrow f=83$.

Answer: (B) 83%

Concept: Same distance, so $\text{Distance}=\text{Speed}\times \text{Time}$ is common to both.

1. Distance $=140\times 13=1820\text{km}$
2. Malaika's time $=\frac{1820}{65}=28$ hours

Trick: For equal distance, time ∝ $\frac{1}{\text{speed}}$: $13\times \frac{140}{65}=13\times \frac{28}{13}=28$.

Answer: (D) 28 hours

Concept: For equal time, profit is shared in the ratio of investments.

1. Ratio $=1310:1350:1140=131:135:114$, total $=380$
2. Dev's share $=\frac{114}{380}\times 1630$
3. $=0.3\times 1630=489$

Trick: $\frac{114}{380}=\frac{3}{10}$ exactly – Dev gets 30% of the profit.

Answer: (C) ₹489

Concept: Shares in a ratio are equal 'parts'; find the value of one part from the given difference.

1. Ratio $12:3:14$; smallest $=3$ parts, largest $=14$ parts.
2. Difference $=14-3=11$ parts $=61699$ ⇒ 1 part $=\frac{61699}{11}=5609$.
3. Total $=(12+3+14)\times 5609=29\times 5609=162661$.

Trick: Total must be a multiple of 29: only $162661=29\times 5609$ works.

Answer: (A) ₹1,62,661

Concept: If $2A=4B=7C=k$, then $A:B:C=\frac{1}{2}:\frac{1}{4}:\frac{1}{7}$.

1. Multiply by LCM $28$: $A:B:C=14:7:4$.
2. Total parts $=14+7+4=25$; 1 part $=\frac{21300}{25}=852$.
3. $A=14\times 852=11928$.

Trick: For $aA=bB=cC$, $A:B:C=bc:ca:ab=28:14:8=14:7:4$.

Answer: (D) ₹11,928

Concept: Increasing a number by $60\%$ means multiplying it by $\frac{160}{100}$.

1. $x\times \frac{160}{100}=3640$.
2. $x=\frac{3640\times 100}{160}=\frac{3640\times 5}{8}=455\times 5=2275$.

Trick: $60\%=\frac{3}{5}$ ⇒ number : new $=5:8$; $\frac{3640}{8}\times 5=2275$.

Answer: (D) $2275$

Concept: In 'buy $x$ get $y$ free', the customer gets $x+y$ items for the price of $x$; effective discount $=\frac{y}{x+y}\times 100\%$.

1. (i) $\frac{3}{8}=37.5\%$; (ii) $\frac{3}{9}=33.3\%$.
2. (iii) $\frac{5}{25}=20\%$; (iv) $\frac{6}{14}=42.86\%$.
3. Highest discount is (iv) – most beneficial.

Trick: Compare $\frac{\text{free}}{\text{total}}$, not $\frac{\text{free}}{\text{bought}}$ – but here both rankings give (iv).

Answer: (C) (iv)

Concept: Consecutive even numbers: $n$ and $n+2$.

1. $n^2+(n+2{)}^2=452$ ⇒ $2n^2+4n+4=452$ ⇒ $n^2+2n-224=0$.
2. $(n+16)(n-14)=0$ ⇒ $n=14$ (natural).
3. Numbers $14,16$: $196+256=452$ ✓; sum $=30$.

Trick: $\frac{452}{2}=226\approx {15}^2$, so numbers lie around $15$: try $14,16$.

Answer: (B) $30$

Concept: Do division and multiplication before addition and subtraction (BODMAS), keeping track of signs.

1. $(-60)÷(-12)=5$ and $(-2)\times 9=-18$.
2. Expression $=-9-5+(-18)$.
3. $=-14-18=-32$.

Trick: Negative ÷ negative = positive; then subtracting a positive moves left on the number line.

Answer: (B) $-32$

Concept: Make the decimal places equal, find the LCM of the whole numbers, then put back the decimal places.

1. $8.6=8.60=\frac{860}{100}$, $0.12=\frac{12}{100}$.
2. $860=2^2\times 5\times 43$, $12=2^2\times 3$ ⇒ $\text{LCM}=2^2\times 3\times 5\times 43=2580$.
3. $\text{LCM}=\frac{2580}{100}=25.80$.

Trick: LCM must be a multiple of $8.6$: $8.6\times 3=25.8$, and $\frac{25.8}{0.12}=215$ ✓.

Answer: (C) $25.8$

Concept: Same time, equal interest: $P_1\times R_1=P_2\times R_2$, so principal is inversely proportional to rate.

1. $P_1\times 12\times 7=P_2\times 13\times 7$ ⇒ $P_1:P_2=13:12$.
2. Total parts $=25$; 1 part $=\frac{20000}{25}=800$.
3. Sum at $12\%$ $=13\times 800=10400$.

Trick: Rates swap into the ratio: rates $12:13$ ⇒ sums $13:12$ (time does not matter).

Answer: (C) ₹10,400

Concept: Volume of a sphere $=\frac{4}{3}\pi r^3$, where $r=\frac{d}{2}$.

1. $r=\frac{12}{2}=6\text{cm}$.
2. $V=\frac{4}{3}\pi \times 6^3=\frac{4}{3}\pi \times 216$.
3. $V=4\times 72\pi =288\pi {\text{cm}}^3$.

Yaad rakhein: Sphere: $V=\frac{4}{3}\pi r^3$, $\text{SA}=4\pi r^2$; hemisphere volume is half.

Answer: (B) $288\pi {\text{cm}}^3$

Concept: Remove brackets by multiplying each term, then combine like terms.

1. $2(\frac{7}{2}{x}^2-28x+17)=7x^2-56x+34$.
2. $-7(x^2+6x-11)=-7x^2-42x+77$.
3. Add: $(7x^2-7x^2)+(-56x-42x)+(34+77)=-98x+111$.

Trick: $x^2$ terms cancel; constant $=34+77=111$ (positive) → only option (C) fits.

Answer: (C) $-98x+111$