RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Equal amounts after different periods: $A(1.1{)}^{12}=B(1.1{)}^{13}$.

1. $A=1.1B\Rightarrow A:B=11:10$.
2. Total parts $=21\Rightarrow$ 1 part $=\frac{1617}{21}=77$.
3. Anil’s share $=11\times 77=847$.

Trick: Gap of 1 year at $10\%$ → shares in ratio $11:10$.

Answer: (A) ₹847

Concept: Ladder, wall and ground form a right triangle; the base is adjacent to the ${60}^{\circ }$ angle.

1. $\cos {60}^{\circ }=\frac{\text{base}}{\text{ladder}}$.
2. $\frac{1}{2}=\frac{4.5}{L}$.
3. $L=9\text{m}$.

Trick: At ${60}^{\circ }$ the hypotenuse is twice the adjacent side.

Answer: (D) $9\text{m}$

Concept: Grouped mode $=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$.

1. Mode 160 is the upper limit of 155-160; take $l=155,f_1=31,f_0=18,f_2=x,h=5$.
2. $160=155+\frac{31-18}{62-18-x}\times 5\Rightarrow \frac{65}{44-x}=5$.
3. $44-x=13\Rightarrow x=31$.

Trick: Mode lies exactly on the boundary 160 only when $f_1=f_2$, so $x=31$.

Answer: (B) 31

Concept: Cross-multiply: $\frac{X}{147}=\frac{48}{X}\Rightarrow X^2=147\times 48$.

1. $147\times 48=7056$.
2. $X=\sqrt{7056}=84$ (positive value).
3. Or: $147\times 48=(49\times 3)(16\times 3)=49\times 16\times 9\Rightarrow X=7\times 4\times 3=84$.

Trick: Split into perfect squares: $49\times 16\times 9$.

Answer: (A) 84

Concept: A biquadratic $x^4+b{x}^2+c=0$ becomes quadratic with $y=x^2$.

1. $y^2-13y+36=0$.
2. $(y-9)(y-4)=0\Rightarrow y=9$ or $y=4$.
3. (Then $x=\pm 3,\pm 2$.)

Trick: Find two numbers with sum 13 and product 36: 9 and 4.

Answer: (A) 9, 4

Concept: Perimeter of a sector $=2r+l$, where arc length $l=r\theta$ ($\theta$ in radians).

1. $r=10.5$, $\theta =\frac{2\pi }{3}$ (i.e. ${120}^{\circ }$).
2. $l=10.5\times \frac{2}{3}\times \frac{22}{7}=7\times \frac{22}{7}=22$
3. Perimeter $=2\times 10.5+22=21+22=43$ cm

Trick: $\frac{2\pi }{3}$ is one-third of the full circle: circumference $=2\times \frac{22}{7}\times 10.5=66$, so arc $=\frac{66}{3}=22$.

Answer: (B) $43$

Concept: Under simple interest the interest is the same every year, so the difference of two amounts gives the interest for the extra years.

1. Interest for 2 years $=3000-1750=1250$, so 1 year $=625$.
2. Principal $=1750-2\times 625=500$
3. Rate $=\frac{625}{500}\times 100=125\%$

Trick: Rate $=\frac{A_2-A_1}{A_1{t}_2-A_2{t}_1}\times 100=\frac{1250}{1750\times 4-3000\times 2}\times 100=\frac{1250}{1000}\times 100=125\%$

Answer: (A) $125\%$

Concept: After successive increases of $a\%$ and $b\%$, value $=x(1+\frac{a}{100})(1+\frac{b}{100})$.

1. $x\times 1.04\times 1.20=156000$
2. $x\times 1.248=156000$
3. $x=\frac{156000}{1.248}=125000$

Trick: Check options: $125000\times 1.04=130000$, $130000\times 1.2=156000$ ✓

Answer: (A) ₹1,25,000

Concept: Remainder theorem: when $p(x)$ is divided by $(x-k)$, the remainder is $p(k)$.

1. $p(2)=a(8)+4(4)+3(2)-4=8a+18$
2. $q(2)=8-14+a=a-6$
3. Equal remainders: $8a+18=a-6\Rightarrow 7a=-24$
4. $a=-\frac{24}{7}$

Trick: Just put $x=2$ in both and equate — no long division needed.

Answer: (B) $-\frac{24}{7}$

Concept: Sum of exterior angles of any polygon $={360}^{\circ }$; sum of interior angles $=(n-2)\times {180}^{\circ }$.

1. 300% more than 360 means $4\times 360={1440}^{\circ }$.
2. $(n-2)\times 180=1440\Rightarrow n-2=8\Rightarrow n=10$
3. Each interior angle $=\frac{1440}{10}={144}^{\circ }$

Trick: Interior : exterior sum $=4:1$ ⇒ each interior : exterior $=4:1$ ⇒ interior $=\frac{4}{5}\times 180={144}^{\circ }$.

Answer: (D) $144$

Concept: $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$; both decimals have 6 places, so they cancel.

1. $\frac{\sqrt{0.018496}}{\sqrt{0.001156}}=\sqrt{\frac{18496}{1156}}$
2. $\sqrt{18496}=136$, $\sqrt{1156}=34$
3. $\frac{136}{34}=4$

Trick: $\frac{18496}{1156}=16$ directly, and $\sqrt{16}=4$.

Answer: (D) $4$

Concept: The largest circle inside a rectangle touches the two longer sides, so its diameter equals the shorter side.

1. Diameter $=63$ m
2. Circumference $=\pi d=\frac{22}{7}\times 63$
3. $=22\times 9=198$ m

Trick: Ignore the longer side (114 m) — only the smaller dimension limits the circle.

Answer: (D) $198$

Concept: Curved surface area of a cylinder $=2\pi rh$.

1. $2\times \frac{22}{7}\times r\times 97=4900$
2. $r=\frac{4900\times 7}{44\times 97}=\frac{34300}{4268}$
3. $r\approx 8.036\approx 8.04$ cm

Trick: Estimate: $2\pi h\approx 6.29\times 97\approx 610$; $\frac{4900}{610}\approx 8.04$.

Answer: (D) $8.04$

Concept: Required number = HCF of (number − its remainder).

1. $93-5=88$, $190-3=187$
2. $88=8\times 11$, $187=17\times 11$
3. HCF $=11$ (and $11>5$, so remainder 5 is valid).

Trick: Check options from the largest: 21, 17, 14 do not divide both 88 and 187; 11 does.

Answer: (D) $11$

Concept: SP at loss $l\%$ $=CP\times \frac{100-l}{100}$; SP at profit $p\%$ $=CP\times \frac{100+p}{100}$.

1. $29=CP\times \frac{25}{100}\Rightarrow CP=116$
2. Required SP $=116\times \frac{175}{100}=203$

Trick: Ratio method: $\text{new SP}=29\times \frac{175}{25}=29\times 7=203$.

Answer: (C) ₹203

Concept: $SP=MP\times \frac{100-d}{100}=CP\times \frac{100+p}{100}$.

1. Let $CP=100$; $SP=184$.
2. $MP\times \frac{40}{100}=184\Rightarrow MP=460$
3. Mark-up $X=\frac{460-100}{100}\times 100=360\%$

Trick: $\frac{MP}{CP}=\frac{100+p}{100-d}=\frac{184}{40}=4.6$ ⇒ $X=360$.

Answer: (B) $360$

Concept: Each seller’s SP is the next buyer’s CP, so the gains multiply: $\text{Retail}=C\times 1.10\times 1.15\times 1.28$.

1. $1.10\times 1.15=1.265$; $1.265\times 1.28=1.6192$
2. $C=\frac{75900}{1.6192}=46875$
3. Check: $46875\to 51562.5\to 59296.875\to 75900$ ✓

Trick: Write as fractions: $C=75900\times \frac{10}{11}\times \frac{20}{23}\times \frac{25}{32}=46875$ — 11 and 23 cancel neatly ($75900=11\times 23\times 300$).

Answer: (C) ₹46,875

Concept: Median = middle value after arranging in order; for odd $n$ it is the ${\left(\frac{n+1}{2}\right)}^{th}$ value.

1. Ascending: 18, 28, 33, 49, 52, 54, 55, 56, 60, 61, 80
2. $n=11$, so median is the $\frac{11+1}{2}=6^{th}$ value.
3. 6th value $=54$

Trick: Never take the middle of the unsorted list (it would give 80) — always sort first.

Answer: (A) $54$

Concept: Divide each option by 47 or build multiples of 47 near the options.

1. $47\times 80=3760$, so $3995-3760=235=47\times 5$
2. $3995=47\times 85$ ✓
3. Others: $3674=47\times 78+8$, $4416=47\times 93+45$, $3816=47\times 81+9$ — not divisible.

Trick: $47\times 85=(50-3)\times 85=4250-255=3995$.

Answer: (C) $3995$

Concept: Net rate = sum of filling rates − emptying rate (part of tank per hour).

1. Net $=\frac{1}{2}+\frac{1}{64}-\frac{1}{2}=\frac{1}{64}$
2. Full tank takes 64 hours.
3. Half tank $=\frac{64}{2}=32$ hours

Trick: The 2-hour filler and 2-hour emptier cancel out; only the 64-hour tap works.

Answer: (B) $32$