RRB NTPC Undergraduate CBT 1 2024 PYQs

Concept: The difference of ratio terms equals the given difference; scale up to the total.

1. Ratio $5:8:17$, total $=30$ parts.
2. Largest − smallest $=17-5=12$ parts $=78106$
3. Total $=\frac{78106}{12}\times 30=78106\times 2.5=195265$

Trick: $\frac{30}{12}=2.5$ – multiply the difference by 2.5 directly.

Answer: (D) ₹1,95,265

Concept: Distance = Speed × Time (convert the units first).

1. $54\text{km/h}=54\times \frac{5}{18}=15\text{m/s}$
2. $1.7\text{min}=1.7\times 60=102\text{s}$
3. Length $=15\times 102=1530\text{m}=1.53\text{km}$

Trick: $54\text{km/h}=0.9\text{km/min}$, so $0.9\times 1.7=1.53\text{km}$.

Answer: (C) 1.53 km

Concept: Two equal cubes joined face to face form a cuboid $2a\times a\times a$; $\text{TSA}=2(lb+bh+hl)$.

1. $l=10$, $b=5$, $h=5$ (cm)
2. $\text{TSA}=2(10\times 5+5\times 5+5\times 10)=2\times 125$
3. $=250{\text{cm}}^2$

Trick: Two cubes have 12 faces; joining hides 2, so TSA $=10a^2=10\times 25=250$.

Answer: (B) $250{\text{cm}}^2$

Concept: Convert each pipe to "tank per hour"; filling pipes are +, emptying pipes are −.

1. P fills $\frac{2}{3}$ in 24 h → full tank in $36\text{h}$; Q: $\frac{2}{3}$ in 16 h → $24\text{h}$.
2. In 4 h, P + Q fill $4(\frac{1}{36}+\frac{1}{24})=4\times \frac{5}{72}=\frac{5}{18}$ of the tank.
3. R empties $\frac{5}{18}$ in 5 h → R empties a full tank in $18\text{h}$.
4. Together: $\frac{1}{36}+\frac{1}{24}-\frac{1}{18}=\frac{2+3-4}{72}=\frac{1}{72}$ → $72\text{h}$

Trick: LCM 72 as capacity: P = 2, Q = 3, R = −4 units/h; net $=1$ unit/h → 72 h.

Answer: (A) 72 hours

Concept: Mean proportional of $a$ and $b$ $=\sqrt{ab}$.

1. $\sqrt{19\times 76}=\sqrt{19\times 19\times 4}$
2. $=19\times 2=38$

Trick: $76=4\times 19$, so the answer is $2\times 19$ without multiplying out.

Answer: (C) 38

Concept: Number to add $=$ divisor − remainder.

1. $41\times 410=16810$
2. $16809=16810-1$, so remainder $=40$.
3. Number to add $=41-40=1$

Trick: Look for a round multiple near the number: $41\times 410=16810$ is just 1 more.

Answer: (C) 1

Concept: If SP of $n$ items = CP of $m$ items, then $\frac{\text{SP}}{\text{CP}}=\frac{m}{n}$.

1. $16\text{SP}=8\text{CP}\Rightarrow \frac{\text{SP}}{\text{CP}}=\frac{8}{16}=\frac{1}{2}$
2. SP < CP → loss.
3. $\text{Loss}\%=\frac{1-\frac{1}{2}}{1}\times 100=50\%$

Trick: $\%=\frac{m-n}{n}\times 100=\frac{8-16}{16}\times 100=-50\%$ (negative = loss).

Answer: (C) $50\%$ loss

Concept: $\text{SI}=\frac{P\times R\times T}{100}$

1. $\text{SI}=\frac{400\times 4\times 5.5}{100}$
2. $=4\times 4\times 5.5=88$

Trick: $4\%$ of 400 = 16 per year; $16\times 5.5=88$.

Answer: (C) 88

Concept: Equivalent discount of $a\%$ and $b\%$ $=a+b-\frac{ab}{100}$.

1. $20+10-\frac{20\times 10}{100}$
2. $=30-2=28\%$

Trick: On ₹100: after $20\%$ → 80; after $10\%$ → 72; total discount $=28\%$.

Answer: (D) $28\%$

Concept: One day's work of C $=\frac{1}{4}-\frac{1}{17}-\frac{1}{16}$.

1. LCM of 4, 17, 16 $=272$.
2. $\frac{68-16-17}{272}=\frac{35}{272}$
3. C alone $=\frac{272}{35}=7\frac{27}{35}$ days

Trick: Total work 272 units: A = 16, B = 17, all = 68 units/day → C $=35$ units/day.

Answer: (B) $7\frac{27}{35}$ days

Concept: Total literates = male literates + female literates.

1. Females $=328000-164000=164000$.
2. Total literates $=24\%\text{ of }328000=78720$.
3. Male literates $=34\%\text{ of }164000=55760$.
4. Female literates $=78720-55760=22960$, so $\frac{22960}{164000}\times 100=14\%$.

Trick: Males = females (half each), so average rule: $\frac{34+x}{2}=24\Rightarrow x=14\%$.

Answer: (D) $14\%$

Concept: A number is divisible by 11 if (sum of digits at odd places) − (sum of digits at even places) is $0$ or a multiple of $11$.

1. N75M52 from the right: odd places $2,M,7$; even places $5,5,N$.
2. Odd sum $=M+9$, even sum $=N+10$.
3. Difference $=(M+9)-(N+10)=M-N-1$.
4. For divisibility, $M-N-1=0\Rightarrow M-N=1$ (e.g. $M=4,N=3$: $375452=11\times 34132$).

Trick: Alternate signs from the right: $2-5+M-5+7-N=M-N-1$.

Answer: (B) $M-N=1$

Concept: Decreasing a number by $6\%$ leaves $94\%$ of it.

1. $94\%\text{ of }x=3760$.
2. $x=\frac{3760\times 100}{94}$.
3. $x=40\times 100=4000$.

Trick: $3760÷94=40$, so the number is $4000$. Check: $6\%$ of $4000=240$, $4000-240=3760$.

Answer: (B) $4000$

Concept: The third proportional $x$ of $a$ and $b$ satisfies $a:b=b:x$, i.e. $x=\frac{b^2}{a}$.

1. $9:60=60:x$.
2. $x=\frac{{60}^2}{9}=\frac{3600}{9}$.
3. $x=400$.

Trick: Third proportional $=\frac{(\text{second}{)}^2}{\text{first}}$.

Answer: (B) $400$

Concept: For consecutive numbers $n(n+1)=P$, $n$ is close to $\sqrt{P}$.

1. $\sqrt{552}\approx 23.5$, so try $23$ and $24$.
2. $23\times 24=552$. ✓
3. Greater number $=24$.

Trick: Unit digit 2 needs ends like $3\times 4$ or $8\times 9$; near $\sqrt{552}$ only $23\times 24$ fits.

Answer: (A) $24$

Concept: Use quick divisibility tests on $630605$.

1. By 5: last digit is $5$ → divisible ✓.
2. By 3: digit sum $6+3+0+6+0+5=20$, not a multiple of $3$ → no.
3. By 14: an odd number cannot be divisible by $14$ (even). By 7: $630605=7\times 90086+3$ → no.

Trick: Last digit 0 or 5 → divisible by 5 at a glance.

Answer: (B) $5$

Concept: All three sides of an equilateral triangle are equal, so perimeter $=3a$.

1. Side $a=13\text{cm}$.
2. Perimeter $=3\times 13=39\text{cm}$.

Trick: Equilateral: $P=3a$; square: $P=4a$.

Answer: (B) $39\text{cm}$

Concept: LCM = product of each factor with its highest power appearing in the numbers.

1. Highest power of $3$: $3^3$; of $8$: $8^3$; of $13$: ${13}^2$; of $16$: ${16}^2$.
2. So LCM $=3^3\times 8^3\times {13}^2\times {16}^2$.
3. Check with primes: $2$-powers are $2^6,2^4,2^{17}$; highest $2^{17}=8^3\times {16}^2$ – same result.

Trick: LCM → highest powers; HCF → lowest powers.

Answer: (A) $3^3\times 8^3\times {13}^2\times {16}^2$

Concept: Apply divisibility tests to $253118139$.

1. By 3: digit sum $2+5+3+1+1+8+1+3+9=33$, a multiple of $3$ → divisible ✓.
2. By 5: last digit $9$ → no. By 8: last three digits $139$ not divisible by $8$ → no.
3. By 12: needs divisibility by 4 and 3; the number is odd → no.

Trick: Odd number → straight away not divisible by 8 or 12.

Answer: (A) $3$

Concept: Sum of first $n$ even numbers $=n(n+1)$, so their average $=n+1$.

1. First 169 even numbers: $2,4,\dots ,338$.
2. Average $=\frac{169\times 170}{169}=170$.
3. Also, average $=\frac{\text{first}+\text{last}}{2}=\frac{2+338}{2}=170$.

Trick: Average of first $n$ even numbers $=n+1$; of first $n$ odd numbers $=n$.

Answer: (A) $170$