SSC CPO Paper I 2020, 2022, 2023, 2024 PYQs

Concept: With simple interest at different rates for different periods, add up rate × time.

1. Total rate-years $=5\times 4+8\times 6+12\times 2=20+48+24=92\%$
2. $92\%$ of P $=9016\Rightarrow P=\frac{9016\times 100}{92}=9800$

Trick: Last part runs only $12-10=2$ years — the usual trap.

Answer: (B) ₹9,800

Concept: Area of an equilateral triangle $=\frac{\sqrt{3}}{4}{a}^2$.

1. $\frac{\sqrt{3}}{4}{a}^2=4\sqrt{3}$
2. $a^2=16\Rightarrow a=4\text{cm}$

Trick: Cancel $\sqrt{3}$ on both sides first: $\frac{a^2}{4}=4$.

Answer: (B) 4

Concept: All colleges have 4 years, so the least average = the least total.

1. A: 68 + 72 + 78 + 80 = 298
2. B: 78 + 86 + 91 + 87 = 342; C: 56 + 78 + 82 + 84 = 300
3. D: 78 + 82 + 85 + 87 = 332. Least total = 298 → College A.

Trick: Compare totals instead of averages when the count is the same; C (300) is the close trap.

Answer: (D) College A

Concept: New person = person replaced + (number of people × increase in average).

1. Total increase $=15\times 3.2=48\text{kg}$
2. New person $=52+48=100\text{kg}$

Trick: Increase in average → add; decrease → subtract.

Answer: (C) 100 kg

Concept: A is what % of B $=\frac{A}{B}\times 100$.

1. From the graph: boys in section B = 30, girls in section E = 55.
2. $\frac{30}{55}\times 100=54.54\%\approx 55\%$

Trick: $\frac{6}{11}\approx 54.5\%$ — remember $\frac{1}{11}=9.09\%$.

Answer: (B) $55\%$

Concept: If $x-\frac{1}{x}=k$, then $x^2+\frac{1}{x^2}=k^2+2$.

1. $x(5-\frac{2}{x})=\frac{5}{x}\Rightarrow 5x-2=\frac{5}{x}$
2. $5x-\frac{5}{x}=2\Rightarrow x-\frac{1}{x}=\frac{2}{5}$
3. $x^2+\frac{1}{x^2}=\frac{4}{25}+2=\frac{54}{25}$

Trick: Minus form → add 2; plus form $(x+\frac{1}{x})$ → subtract 2.

Answer: (A) $\frac{54}{25}$

Concept: The largest square tile that fits both length and breadth exactly has side = HCF of the two.

1. $126=2\times 3^2\times 7$, $90=2\times 3^2\times 5$
2. $\text{HCF}=2\times 9=18\text{ft}$
3. Area of each tile $={18}^2=324\text{sq ft}$

Trick: Largest tile → HCF; least number of tiles = (area of floor) ÷ (tile area).

Answer: (C) 324

Concept: Check each column: every next value must be larger than the previous one.

1. Wheat: 62 → 81 → 116 → 124 → 137 (rises every time).
2. Rice falls 197 → 187; coarse grains keep falling; pulses fall 64 → 46 → 44.

Trick: One single fall is enough to reject an option.

Answer: (D) Wheat

Concept: LCM of two distinct primes = their product.

1. $533=13\times 41$, so $x=41$, $y=13$ ($x>y$).
2. $4y-x=52-41=11$

Trick: To factor 533, test primes up to $\sqrt{533}\approx 23$: $533÷13=41$.

Answer: (B) 11

Concept: If $A+B={90}^{\circ }$: $\cot B=\tan A$ and $\cos B=\sin A$.

1. $\frac{\cot A}{\cot B}=\frac{\cot A}{\tan A}={\cot }^{2}A$
2. ${\cos }^{2}A+{\cos }^{2}B={\cos }^{2}A+{\sin }^{2}A=1$
3. Expression $=1+{\cot }^{2}A={\csc }^{2}A$

Trick: Check with $A=B={45}^{\circ }$: $1+\frac{1}{2}+\frac{1}{2}=2={\csc }^2{45}^{\circ }$ — only (B) and (D) give 2; (B) matches in general.

Answer: (B) ${\csc }^{2}A$

Concept: Compare work done per day (efficiency) of the two persons.

1. Let Parul do $W$ in time $t$; Ramesh does $\frac{W}{2}$ in $\frac{4t}{5}$.
2. Ramesh's rate $=\frac{W/2}{4t/5}=\frac{5}{8}·\frac{W}{t}$ ⇒ Parul : Ramesh $=8:5$
3. Total work $=(8+5)\times 24=312$ units
4. Parul alone $=\frac{312}{8}=39$ days

Trick: Efficiency ratio = $\frac{\text{work ratio}}{\text{time ratio}}=\frac{1/2}{4/5}=\frac{5}{8}$.

Answer: (D) 39 days

Concept: Compare the 'Total' row of the table and choose the smallest.

1. Totals: A = 5825, B = 5703, C = 5424, D = 5613, E = 5625.
2. The smallest total is 5424, for organisation C.

Trick: When a Total row is given, use it directly instead of adding six departments.

Answer: (A) C

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

1. $(\sin \theta +\cos \theta {)}^2=\frac{11}{9}$
2. $(\cos \theta -\sin \theta {)}^2=2-\frac{11}{9}=\frac{7}{9}$
3. $\cos \theta -\sin \theta =\frac{\sqrt{7}}{3}$

Trick: Sum of the two squares is always 2 — subtract and take the root.

Answer: (D) $\frac{\sqrt{7}}{3}$

Concept: Solve brackets first, then division/multiplication left to right.

1. $48÷72\times 3=\frac{2}{3}\times 3=2$
2. $15÷8\times 8-10=15-10=5$
3. $2-5+2P=3\Rightarrow 2P=6\Rightarrow P=3$

Trick: $÷$ and $\times$ go left to right: $15÷8\times 8=15$.

Answer: (A) 3

Concept: Difference in profit % corresponds to the difference in selling price.

1. $57\%-7\%=50\%$ of CP $=1329$
2. $\text{CP}=1329\times 2=2658$

Trick: $50\%$ means just double the amount.

Answer: (B) 2658

Concept: Simplify a continued fraction from the bottom upward.

1. $2+\frac{1}{3}=\frac{7}{3}$, so $\frac{1}{7/3}=\frac{3}{7}$
2. $1+\frac{3}{7}=\frac{10}{7}$, so $\frac{1}{10/7}=\frac{7}{10}$
3. $A=\frac{9}{10}-\frac{7}{10}=\frac{2}{10}=\frac{1}{5}$

Trick: Always start from the lowest fraction and flip upward.

Answer: (A) $\frac{1}{5}$

Concept: Diagonals of a rhombus bisect each other at right angles; area $=\frac{1}{2}{d}_1{d}_2$.

1. Side $=\frac{52}{4}=13\text{cm}$; half of $d_1=5$
2. Half of $d_2=\sqrt{{13}^2-5^2}=12\Rightarrow d_2=24$
3. Area $=\frac{1}{2}\times 10\times 24=120{\text{cm}}^2$

Trick: 5-12-13 is a Pythagorean triplet — spot it instantly.

Answer: (A) $120{\text{cm}}^2$

Concept: Downstream speed $=B+S$, upstream speed $=B-S$.

1. Downstream $=20+8=28\text{km/h}$, upstream $=20-8=12\text{km/h}$
2. $\frac{d}{12}-\frac{d}{28}=6\Rightarrow d·\frac{7-3}{84}=6$
3. $d=\frac{6\times 84}{4}=126\text{km}$

Trick: Shortcut: $d=\frac{t\times \text{up}\times \text{down}}{\text{down}-\text{up}}=\frac{6\times 12\times 28}{16}=126$.

Answer: (C) 126 km

Concept: In a two-candidate contest, the margin is the difference of their vote percentages.

1. P = $40\%$, Q = $60\%$; margin $=20\%$
2. $20\%$ of total $=10\Rightarrow$ total $=50$

Trick: Margin % = $100-2\times (\text{loser}\%)$.

Answer: (B) 50

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

1. $\text{SP}=1250\times 0.86=1075$
2. $\text{CP}=\frac{1075\times 100}{114}=942.98\approx 943$

Trick: Equal discount% and profit% do NOT cancel: $\text{CP}=\text{MP}\times \frac{86}{114}$, not MP.

Answer: (D) ₹943