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

Concept: Change in average $=\frac{\text{change in total}}{\text{number of items}}$.

1. Excess entered $=99-66=33$
2. Increase in average $=\frac{33}{55}=0.6$

Trick: Only the error matters, not the actual marks of others.

Answer: (C) $0.6$

Concept: Saving $=$ Income $-$ Expenditure. Take income $=100$.

1. Old: income $100$, expense $68$, saving $32$
2. New: income $115$, expense $68\times 1.1=74.8$, saving $40.2$
3. Increase $=\frac{40.2-32}{32}\times 100=\frac{8.2}{32}\times 100=25.625\%$
4. To 2 decimal digits: $25.62\%$

Trick: Assume income $=100$ so every figure is directly a percentage.

Answer: (D) $25.62\%$

Concept: Volume of a sphere $=\frac{4}{3}\pi r^3$; number of small spheres $=\frac{V_{\text{big}}}{V_{\text{small}}}={\left(\frac{R}{r}\right)}^3$.

1. $\frac{R}{r}=\frac{5}{2.5}=2$
2. Number $=2^3=8$

Trick: Halving the radius gives $8$ times as many spheres.

Answer: (A) $8$

Concept: Sum of angles of a triangle $={180}^{\circ }$.

1. Let smallest $=x$; others $2x$ and $3x$
2. $x+2x+3x=6x={180}^{\circ }$
3. $x={30}^{\circ }$

Yaad rakhein: Ratio $1:2:3$ always gives ${30}^{\circ },{60}^{\circ },{90}^{\circ }$.

Answer: (C) ${30}^{\circ }$

Concept: Surface area of sphere $=4\pi r^2$; rate $=\frac{\text{total cost}}{\text{area}}$.

1. $r=\frac{14}{2}=7\text{cm}$
2. Area $=4\times \frac{22}{7}\times 49=616{\text{cm}}^2$
3. Rate $=\frac{21560}{616}=35$

Trick: For $r=7$, $4\pi r^2=616$ — worth remembering.

Answer: (B) ₹$35$

Concept: Opposite directions: relative speed $=$ sum of speeds; distance $=$ sum of lengths.

1. Relative speed $=42+48=90\text{km/h}=90\times \frac{5}{18}=25\text{m/s}$
2. Distance $=230+270=500\text{m}$
3. Time $=\frac{500}{25}=20\text{s}$

Trick: Multiply km/h by $\frac{5}{18}$ to get m/s.

Answer: (B) $20$ seconds

Concept: $x^3+y^3+z^3-3xyz=\frac{1}{2}(x+y+z)[(x-y{)}^2+(y-z{)}^2+(z-x{)}^2]$.

1. $x+y+z=110+111+112=333$
2. $(x-y{)}^2+(y-z{)}^2+(z-x{)}^2=1+1+4=6$
3. Value $=\frac{1}{2}\times 333\times 6=999$

Trick: For three consecutive numbers the value is always $3\times$ their sum.

Answer: (A) $999$

Concept: MP $=$ CP $\times (1+\text{markup})$; SP $=$ MP $\times (1-\text{discount})$.

1. MP $=1600\times 2.3=3680$
2. SP $=3680\times 0.75=2760$

Trick: Net factor $=2.3\times 0.75=1.725$; $1600\times 1.725=2760$.

Answer: (A) $2760$

Concept: Add each row, then subtract.

1. Cricket $=100+150+200+300+200=950$
2. Tennis $=200+220+210+210+230=1070$
3. Difference $=1070-950=120$

Trick: Subtract column-wise: $100-20-10+90-30=120$ (Tennis − Cricket).

Answer: (A) $120$

Concept: Downstream $D=B+S$, upstream $U=B-S$, stream $S=\frac{D-U}{2}$.

1. $D=\frac{2}{10/60}=12\text{km/h}$
2. $U=\frac{12}{2}=6\text{km/h}$
3. $S=\frac{12-6}{2}=3\text{km/h}$

Trick: Stream speed is half the difference of downstream and upstream speeds.

Answer: (C) $3\text{km/h}$

Concept: Loser $35\%$, winner $65\%$; margin $=30\%$ of votes polled.

1. $65\%-35\%=30\%$
2. $30\%$ of total $=15900$
3. Total $=\frac{15900}{0.3}=53000$

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

Answer: (D) $53,000$

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. $2-\frac{3}{7}=\frac{11}{7}$, so $\frac{1}{11/7}=\frac{7}{11}$
3. $1+\frac{7}{11}=\frac{18}{11}$, so $\frac{1}{18/11}=\frac{11}{18}$
4. $1-\frac{11}{18}=\frac{7}{18}$

Trick: Each step: reciprocal of the lower result.

Answer: (A) $\frac{7}{18}$

Concept: Let upstream speed $=u$, downstream $=d$; use $\frac{1}{u}=a$, $\frac{1}{d}=b$ to make the equations linear.

1. $24a+36b=10$ and $36a+24b=12$
2. Adding: $60(a+b)=22\Rightarrow a+b=\frac{11}{30}$; subtracting: $12(a-b)=2\Rightarrow a-b=\frac{1}{6}$
3. $a=\frac{4}{15}\Rightarrow u=\frac{15}{4}$; $b=\frac{1}{10}\Rightarrow d=10$
4. Current $=\frac{d-u}{2}=\frac{10-3.75}{2}=\frac{25}{8}\text{km/h}$

Trick: Swapped coefficients ($24,36$ / $36,24$): add and subtract the equations.

Answer: (D) $\frac{25}{8}\text{km/h}$

Concept: At CI, if money becomes $k$ times in $n$ years, it becomes $k^m$ times in $mn$ years.

1. $3$ times in $5$ years
2. $9=3^2$ times in $2\times 5=10$ years

Trick: Powers multiply the time: $3\to 9\to 27$ in $5,10,15$ years.

Answer: (B) $10$ years

Concept: Solve innermost brackets first; $(-)\times (-)=(+)$.

1. $9-(6-2)=5$; $(-4)\times 5=-20$; $25-(-20)=45$
2. $(-3)\times (-3)=9$; $6+9=15$; $3\times 15=45$
3. $45÷45=1$

Trick: Watch the double negative: $25-(-20)=25+20$.

Answer: (A) $1$

Concept: Bracket first, then division.

1. $\frac{13}{4}\times 80=260$
2. $260-\frac{91}{4}=\frac{1040-91}{4}=\frac{949}{4}$
3. $1898÷\frac{949}{4}=\frac{1898\times 4}{949}=2\times 4=8$

Trick: Notice $1898=2\times 949$.

Answer: (B) $8$

Concept: Average $=\frac{\text{sum}}{5}$; values are in hundreds.

1. Demand: $35+25+30+30+40=160\Rightarrow$ average $32$
2. Production: $30+40+25+40+45=180\Rightarrow$ average $36$
3. Difference $=4$ hundred $=400$

Trick: Difference of averages $=\frac{180-160}{5}=4$ hundred.

Answer: (D) $400$

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

1. SI $=4900-2500=2400$
2. $2400=\frac{2500\times 12\times T}{100}=300T$
3. $T=8$ years

Trick: Yearly SI $=12\%$ of $2500=300$; $\frac{2400}{300}=8$.

Answer: (C) $8$

Concept: Cone $=\frac{1}{3}\pi r^{2}h$, cylinder $=\pi r^{2}h$; $\pi$ cancels in the ratio.

1. Cone $=\frac{1}{3}\pi \times 25\times 6=50\pi$
2. Cylinder $=\pi \times 6.25\times 3=18.75\pi$
3. Ratio $=\frac{50}{18.75}=\frac{8}{3}$

Trick: $\frac{1}{3}\times \frac{5^2\times 6}{{2.5}^2\times 3}=\frac{1}{3}\times 4\times 2=\frac{8}{3}$.

Answer: (D) $8:3$

Concept: $a^2-b^2=(a+b)(a-b)$ and $a^2-2ab+b^2=(a-b{)}^2$ with $a=3.2$, $b=0.2$.

1. Numerator $=(3.2+0.2)(3.2-0.2)=3.4\times 3$
2. Denominator $=(3.2-0.2{)}^2=9$
3. Value $=\frac{3.4\times 3}{9}=\frac{3.4}{3}=\frac{17}{15}$

Trick: Expression $=\frac{a+b}{a-b}=\frac{3.4}{3.0}$.

Answer: (C) $\frac{17}{15}$