RRB NTPC Undergraduate CBT 1 2024 PYQs

Concept: $\text{HCF}\times \text{LCM}=\text{product of the two numbers}$.

1. $11\times 330=66\times x$
2. $x=\frac{3630}{66}=55$

Trick: Other number must be a multiple of HCF 11 dividing 330 → 55.

Answer: (B) 55

Concept: Find each pipe's full-tank time, then add rates (emptying pipe negative).

1. P: $\frac{3}{8}$ in 21 h → full in $21\times \frac{8}{3}=56$ h; Q: $\frac{2}{7}$ in 16 h → $56$ h.
2. In 2 h: $2(\frac{1}{56}+\frac{1}{56})=\frac{1}{14}$ tank filled.
3. R empties $\frac{1}{14}$ in 3 h → empties full tank in 42 h.
4. Together: $\frac{1}{56}+\frac{1}{56}-\frac{1}{42}=\frac{3+3-4}{168}=\frac{1}{84}$ → 84 h.

Trick: Take tank $=168$ units: P = 3, Q = 3, R = −4 per hour → net 2 → $\frac{168}{2}=84$ h.

Answer: (D) 84 hours

Concept: Pythagoras: ${\text{base}}^2+{\text{height}}^2={\text{hypotenuse}}^2$; area $=\frac{1}{2}\times \text{base}\times \text{height}$.

1. Sides $x$ and $2x$: $x^2+4x^2={15}^2$
2. $5x^2=225\Rightarrow x^2=45$
3. Area $=\frac{1}{2}\times x\times 2x=x^2=45{\text{cm}}^2$

Trick: No need to find $x$ – area equals $x^2$ directly.

Answer: (C) 45

Concept: Equal terms with opposite signs cancel; then simplify the complex fraction.

1. $\frac{5}{3}$ and $-\frac{5}{3}$ cancel.
2. $1+\frac{5}{6}=\frac{11}{6}$
3. $\frac{1}{\frac{11}{6}}=\frac{6}{11}$

Trick: Spot cancellations before computing.

Answer: (B) $\frac{6}{11}$

Concept: $\text{Average}=\frac{\text{sum}}{\text{count}}$.

1. Sum $=40+49+56+76+38=259$
2. Average $=\frac{259}{5}=51.8\text{kg}$

Trick: Assume 50: deviations $-10,-1,+6,+26,-12$ sum $=9$ → $50+\frac{9}{5}=51.8$.

Answer: (D) 51.8

Concept: Profit ratio = capital × time ratio.

1. $M+N=4920,M-N=328\Rightarrow M=2624,N=2296$ → ratio $8:7$
2. $\frac{3m}{7n}=\frac{8}{7}\Rightarrow 3m=8n$ (capitals $m,n$)
3. $m=n+50000\Rightarrow 3n+150000=8n\Rightarrow n=30000$
4. $m=80000$

Trick: $2624:2296$ — divide both by 328 → $8:7$.

Answer: (C) ₹80,000

Concept: Profit = total SP − total CP (broken items give no revenue).

1. Bottles left $=50-28=22$
2. SP $=22\times 5.80=127.60$
3. Profit $=127.60-50=77.60$

Trick: Cost stays ₹50 even though bottles broke.

Answer: (D) ₹77.60

Concept: Combined average $=\frac{\text{total runs}}{\text{total matches}}$.

1. Runs in 23 matches $=23\times 42=966$
2. Runs in 10 matches $=130$
3. Average $=\frac{1096}{33}\approx 33.21$

Trick: Answer must lie between 13 and 42, nearer 42 (more matches) → only 33.21 fits the exact division.

Answer: (C) 33.21

Concept: Simplify the complex fraction and combine like fractions.

1. $\frac{1}{1+\frac{5}{6}}=\frac{6}{11}$
2. $\frac{4}{5}-\frac{2}{5}=\frac{2}{5}$
3. $\frac{2}{5}+\frac{6}{11}=\frac{22+30}{55}=\frac{52}{55}$

Trick: Group same-denominator fractions first.

Answer: (A) $\frac{52}{55}$

Concept: Interior + exterior $={180}^{\circ }$; number of sides $n=\frac{{360}^{\circ }}{\text{exterior}}$.

1. $I+E={180}^{\circ },I-E={120}^{\circ }$
2. $2E={60}^{\circ }\Rightarrow E={30}^{\circ }$
3. $n=\frac{360}{30}=12$

Trick: Exterior $=\frac{180-\text{difference}}{2}$.

Answer: (B) 12

Concept: When all invest for the same time, profit is shared in the ratio of investments.

1. Total investment $=1200+1070+1310=3580$.
2. Profit $1790=\frac{3580}{2}$, i.e. profit is exactly half of the investment.
3. Tejas's share $=\frac{1310}{3580}\times 1790=\frac{1310}{2}=655$.

Trick: Spot that profit = half of total capital, so each share = half of own capital.

Answer: (D) ₹655

Concept: Use $(1+\cos \theta )(1-\cos \theta )={\sin }^2\theta$ and $(1+\sin \theta )(1-\sin \theta )={\cos }^2\theta$.

1. $X=\frac{2(1+\cos \theta )(1-\cos \theta )}{2(1+\sin \theta )(1-\sin \theta )}=\frac{{\sin }^2\theta }{{\cos }^2\theta }={\tan }^2\theta$.
2. $X+\frac{1}{X}+2={\tan }^2\theta +{\cot }^2\theta +2=(\tan \theta +\cot \theta {)}^2$.
3. $\tan \theta +\cot \theta =\frac{{\sin }^2\theta +{\cos }^2\theta }{\sin \theta \cos \theta }=\sec \theta \text{cosec}\theta$, so the value is ${\text{cosec}}^2\theta {\sec }^2\theta$.

Trick: Put $\theta ={45}^{\circ }$: $X=1$, value $=4$; only ${\text{cosec}}^2\theta {\sec }^2\theta =2\times 2=4$ matches.

Answer: (D) ${\text{cosec}}^2\theta {\sec }^2\theta$

Concept: Under compound interest, if a sum becomes $k$ times in $t$ years, it becomes $k^n$ times in $nt$ years.

1. 3 times in 17 years.
2. $81=3^4$, so the sum must triple 4 times.
3. Time $=4\times 17=68$ years.

Trick: Write the target as a power of the base multiple: $3\to 81=3^4\Rightarrow 4\times 17$.

Answer: (A) 68 years

Concept: Evaluate powers and roots first, then add/subtract (BODMAS).

1. $8^2=64$, $\sqrt{3^2}=3$, $2\sqrt{36}=2\times 6=12$.
2. $64+3-12-11=44$.

Trick: $\sqrt{a^2}=a$ for positive $a$ – no need to square and root again.

Answer: (D) 44

Concept: In 'Buy $x$ get $y$ free', the customer pays for $x$ but receives $x+y$ articles.

1. Articles received $=20+5=25$; articles free $=5$.
2. $\text{Discount}\%=\frac{5}{25}\times 100=20\%$.

Trick: $\text{Discount}\%=\frac{\text{free}}{\text{paid}+\text{free}}\times 100$ – not $\frac{5}{20}$ (that gives the tempting 25%).

Answer: (C) 20%

Concept: Expand the brackets; the $x^2$ terms cancel, leaving a linear equation.

1. $5(5x^2-5)=25x^2-25$ and $5(5x^2+7x-2)=25x^2+35x-10$.
2. Difference: $25x^2-25-25x^2-35x+10=-35x-15$.
3. $-35x-15=14\Rightarrow -35x=29\Rightarrow x=-\frac{29}{35}$.

Trick: Take 5 common: $5[(5x^2-5)-(5x^2+7x-2)]=5(-7x-3)=14$.

Answer: (A) $-\frac{29}{35}$

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

1. $2.8=2.800=\frac{2800}{1000}$, $0.217=\frac{217}{1000}$.
2. $2800=2^4\times 5^2\times 7$, $217=7\times 31$.
3. $\text{LCM}(2800,217)=2^4\times 5^2\times 7\times 31=86800$.
4. LCM $=\frac{86800}{1000}=86.8$.

Trick: The LCM must be a multiple of 2.8: $2.8\times 31=86.8$, and $0.217\times 400=86.8$ ✓.

Answer: (D) 86.8

Concept: Form two linear equations with son's age $s$ and father's age $f$.

1. $4s+f=100$ … (i); $s+2.5f=97$ … (ii).
2. From (ii): $s=97-2.5f$. Put in (i): $388-10f+f=100$.
3. $9f=288\Rightarrow f=32$ (and $s=17$).

Trick: Check options in (i): $f=32\Rightarrow s=17$; then $17+2.5\times 32=97$ ✓.

Answer: (B) 32

Concept: Convert everyone into one type of worker using total work (man-days = woman-days).

1. Work $=4\times 12=48$ man-days $=8\times 15=120$ woman-days.
2. So $1\text{ man}=\frac{120}{48}=2.5$ women; $2\text{ men}=5$ women.
3. $2$ men $+3$ women $=8$ women; time $=\frac{120}{8}=15$ days.

Trick: Equate 48 M = 120 W → M : W efficiency = 5 : 2.

Answer: (B) 15 days

Concept: For a regular polygon, exterior angle $=\frac{{360}^{\circ }}{n}$ and interior + exterior $={180}^{\circ }$.

1. Exterior angle $={180}^{\circ }-{162}^{\circ }={18}^{\circ }$.
2. $n=\frac{{360}^{\circ }}{{18}^{\circ }}=20$.

Trick: Always go via the exterior angle – it gives $n$ in one division.

Answer: (C) 20