RRB NTPC Undergraduate CBT 1 2024 PYQs

Concept: Work on the part of salary left after each payment.

1. Let salary $=S$. After debt: $S-36\%S=0.64S$.
2. He spends $50\%$ of this, so savings $=0.5\times 0.64S=0.32S$.
3. $0.32S=704\Rightarrow S=\frac{704}{0.32}=2200$.

Trick: Savings fraction $=0.64\times 0.5=0.32$ of salary; divide savings by $0.32$ directly.

Answer: (C) ₹2,200

Concept: $\text{Distance}=\text{Speed}\times \text{Time}$, with time in hours.

1. Time $=18$ min $=\frac{18}{60}=0.3$ h.
2. Length of bridge $=21\times 0.3=6.3\text{km}$.

Trick: 18 min $=\frac{3}{10}$ h, so distance $=\frac{3}{10}$ of the speed: $\frac{3\times 21}{10}=6.3$.

Answer: (C) 6.3 km

Concept: Follow BODMAS: innermost bracket first, then multiplication, then addition, then division.

1. $(3-4)=-1$.
2. $7\times (-1)=-7$, so $\{13-7\}=6$.
3. $138÷6=23$.

Yaad rakhein: Solve brackets from inside out: ( ) → { } → [ ].

Answer: (A) 23

Concept: Take total work = LCM of the days; find the work done together and subtract.

1. Total work $=\text{LCM}(11,23)=253$ units.
2. A does $\frac{253}{11}=23$ units/day, B does $\frac{253}{23}=11$ units/day; together $34$ units/day.
3. In 2 days: $68$ units. Left $=253-68=185$ units $=\frac{185}{253}$.

Trick: Work left $=1-2(\frac{1}{11}+\frac{1}{23})=1-\frac{68}{253}$.

Answer: (C) $\frac{185}{253}$

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

1. Write with 3 decimal places: $2.900$ and $0.031$ → $2900$ and $31$.
2. $2900=2^2\times 5^2\times 29$ and $31$ is prime, so $\text{LCM}=2900\times 31=89900$.
3. Put back 3 decimal places: $89.900=89.9$.

Trick: LCM of decimals $=\frac{\text{LCM of numerators}}{\text{HCF of denominators}}$: $\frac{\text{LCM}(29,31)}{\text{HCF}(10,1000)}=\frac{899}{10}=89.9$.

Answer: (A) 89.9

Concept: Volume is conserved: number of balls $=\frac{\text{volume of big sphere}}{\text{volume of one ball}}$.

1. Big sphere radius $R=\frac{64}{2}=32$ cm, ball radius $r=4$ cm.
2. $n=\frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}={\left(\frac{32}{4}\right)}^3=8^3=512$.

Trick: For spheres, $n={\left(\frac{R}{r}\right)}^3$ — no need to use $\pi$.

Answer: (D) 512

Concept: If $2A=4B=7C$, the shares are in the ratio $\frac{1}{2}:\frac{1}{4}:\frac{1}{7}$.

1. Multiply by LCM 28: $A:B:C=14:7:4$; total parts $=25$.
2. One part $=\frac{45800}{25}=1832$.
3. Share of A $=14\times 1832=25648$.

Trick: $xA=yB=zC\Rightarrow A:B:C=yz:xz:xy=28:14:8=14:7:4$.

Answer: (C) ₹25,648

Concept: Number to add $=\text{divisor}-\text{remainder}$.

1. $76\times 262=19912$, so $19964-19912=52$ is the remainder.
2. Number to add $=76-52=24$; check: $19988=76\times 263$.

Yaad rakhein: Least to add $=d-r$; least to subtract $=r$.

Answer: (C) 24

Concept: $\text{Sum}=\text{Average}\times \text{Count}$.

1. First two numbers: $80\times 2=160$; third $=106$.
2. Last two: $655-160-106=389$.
3. Average $=\frac{389}{2}=194.5$.

Trick: Remove known parts from the total, then divide by the count left.

Answer: (C) 194.5

Concept: Successive discounts are applied one after another on the reduced price.

1. After $20\%$: $1200\times 0.8=960$.
2. After $10\%$: $960\times 0.9=864$.

Trick: Net discount of $20\%$ and $10\%$ $=20+10-\frac{20\times 10}{100}=28\%$; $72\%$ of 1200 $=864$.

Answer: (D) ₹864

Concept: Convert days to one-day work and subtract to get each person's rate.

1. Kiran $=\frac{1}{26}$; Kiran + Garima $=\frac{1}{13}$ ⇒ Garima $=\frac{1}{13}-\frac{1}{26}=\frac{1}{26}$.
2. Mehak $=\frac{1}{10}-\frac{1}{13}=\frac{3}{130}$.
3. Kiran + Mehak $=\frac{1}{26}+\frac{3}{130}=\frac{5+3}{130}=\frac{8}{130}=\frac{4}{65}$ ⇒ $\frac{65}{4}$ days.

Trick: Take total work $=130$ units: K $=5$, K+G $=10$, K+G+M $=13$ ⇒ M $=3$, K+M $=8$ ⇒ $\frac{130}{8}=\frac{65}{4}$.

Answer: (C) $\frac{65}{4}$ days

Concept: Write the equality and solve for $\frac{a}{b}$.

1. $\frac{43}{100}a=\frac{2}{9}b$.
2. $\frac{a}{b}=\frac{2}{9}\times \frac{100}{43}=\frac{200}{387}$.

Trick: $a\times p=b\times q\Rightarrow a:b=q:p$; here $\frac{2}{9}:\frac{43}{100}=200:387$.

Answer: (C) $200:387$

Concept: Know the family of quadrilaterals and their properties.

1. (i) False: every square IS a rhombus (all sides equal).
2. (ii) False: a trapezium has one pair of parallel sides, not two pairs of equal opposite sides.
3. (iii) True: a rhombus is a parallelogram with all sides equal.
4. (iv) False: diagonals are equal only in rectangles and squares.

Yaad rakhein: Square ⊂ Rhombus ⊂ Parallelogram; Square ⊂ Rectangle ⊂ Parallelogram.

Answer: (B) iii

Concept: Equal interest for equal time ⇒ $P_1\times R_1=P_2\times R_2$.

1. $P_1\times 12=P_2\times 8\Rightarrow P_1:P_2=2:3$.
2. Sum at $12\%=\frac{2}{5}\times 22400=8960$.

Trick: Principals are in the inverse ratio of the rates: $8:12=2:3$.

Answer: (A) ₹8,960

Concept: Express list price and selling price in terms of cost price.

1. Let CP $=100x$. List price $=144x$.
2. SP $=75\%$ of $144x=108x$ ⇒ profit $=8x=67$ ⇒ $x=8.375$.
3. List price $=144\times 8.375=1206$.

Trick: $\text{LP}=\frac{144}{8}\times \text{profit}=18\times 67=1206$.

Answer: (A) ₹1,206

Concept: $V=\pi r^{2}h$, so the new volume factor $=(\text{radius factor}{)}^2\times \text{height factor}$.

1. Radius factor $=0.72$, height factor $=2.41$.
2. New $V={0.72}^2\times 2.41=0.5184\times 2.41=1.2493$ times.
3. Increase $\approx 24.93\%\approx 25\%$.

Trick: Multiply factors: $(1-0.28{)}^2(1+1.41)$, then subtract 1.

Answer: (D) $25\%$

Concept: Compute each quantity separately and subtract.

1. $65\%$ of $75=\frac{65\times 75}{100}=48.75$.
2. $\frac{3}{5}$ of $55=33$.
3. Difference $=48.75-33=15.75$.

Trick: $65\%$ of 75 = $75\%$ of 65 $=48.75$ (swap trick).

Answer: (D) 15.75

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

1. Other number $=\frac{3\times 396}{132}=\frac{1188}{132}=9$.
2. Check: $\text{HCF}(132,9)=3$, $\text{LCM}=396$ ✓.

Yaad rakhein: $a\times b=H\times L$ — works only for two numbers.

Answer: (D) 9

Concept: Overheads (decoration) are added to the cost price.

1. CP $=743+8=751$; SP $=750$ ⇒ loss $=1$.
2. Loss $\%=\frac{1}{751}\times 100=\frac{100}{751}\%$.

Trick: Always add repair/transport/decoration cost to CP before finding profit or loss.

Answer: (A) $\frac{100}{751}\%$ loss

Concept: Apply divisibility tests to 242425.

1. Last digit 5 ⇒ divisible by 5 ✓.
2. It is odd ⇒ not divisible by 2, hence not by 6.
3. Digit sum $=2+4+2+4+2+5=19$ ⇒ not divisible by 9.

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

Answer: (D) 5