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

Concept: Half-yearly compounding: rate $=\frac{R}{2}$, periods $=2n$.

1. Rate $=5\%$ per half-year, 4 periods.
2. $A=6500\times (1.05{)}^4=6500\times 1.21550625$
3. $A\approx 7900.79$ ⇒ ₹7,900 (integral value)

Trick: Effective CI for 4 periods at 5% $\approx 21.55\%$; $6500\times 21.55\%\approx 1400.8$.

Answer: (D) ₹7,900

Concept: If A takes 2.4 times the time of (B + C), A's rate $=\frac{\text{rate of }(B+C)}{2.4}$.

1. Let B's one-day work $=b$; C $=\frac{1}{75}$.
2. $A=\frac{b+\frac{1}{75}}{2.4}$ and $A+b=\frac{1}{27}$.
3. $b+\frac{1}{75}+2.4b=\frac{2.4}{27}\Rightarrow 3.4b=\frac{8}{90}-\frac{1}{75}=\frac{34}{450}$
4. $b=\frac{1}{45}$ ⇒ B alone takes 45 days.

Trick: Check: B = 45 days, A + B = 27 ⇒ A = $\frac{1}{27}-\frac{1}{45}=\frac{1}{67.5}$; B + C $=\frac{1}{45}+\frac{1}{75}=\frac{1}{28.125}$, and $67.5=2.4\times 28.125$ ✓.

Answer: (C) 45

Concept: If two circles touch externally at C and AB is a direct common tangent, then $\angle ACB={90}^{\circ }$ always.

1. Draw the common tangent at C meeting AB at M: $MA=MC=MB$ (tangents from one point are equal).
2. So $\angle MAC=\angle MCA$ and $\angle MBC=\angle MCB$.
3. Angle sum in $△ACB$: $2(\angle MCA+\angle MCB)={180}^{\circ }\Rightarrow \angle ACB={90}^{\circ }$.

Yaad rakhein: The 55° is extra data – it only gives $\angle CBA={35}^{\circ }$; $\angle ACB$ is always 90°.

Answer: (B) 90°

Concept: Percentage is taken on the total number of boys only.

1. Total boys $=25+20=45$
2. Boys not in Science $=20$
3. $\frac{20}{45}\times 100=\frac{400}{9}\approx 44.44\%$

Trick: $\frac{4}{9}=0.444\dots$; using all 95 students instead of 45 boys is the common mistake.

Answer: (D) 44.44%

Concept: Quantity of a sector = sector % × total.

1. Grapes $=10\%$, Oranges $=15\%$.
2. Difference $=5\%$ of 1200 kg
3. $=\frac{5}{100}\times 1200=60\text{kg}$

Trick: Find the % difference first, then convert once.

Answer: (A) 60

Concept: Add the two organisations for each year, then simplify the ratio.

1. 2019: D + E $=7000+6600=13600$
2. 2021: D + E $=8000+7600=15600$
3. $13600:15600=136:156=34:39$

Trick: 2019 total is smaller, so the first term must be smaller – rules out 39 : 34 and 14 : 9.

Answer: (D) 34 : 39

Concept: $\tan \theta +\frac{1}{\tan \theta }=2\Rightarrow (\tan \theta -1{)}^2=0\Rightarrow \tan \theta =1$, so $\theta ={45}^{\circ }$ and $\cot \theta =1$.

1. Every power of 1 is 1.
2. $2(1)+3(1)+5(1)(1)$
3. $=2+3+5=10$

Trick: $x+\frac{1}{x}=2$ ⇒ $x=1$; then just add the coefficients.

Answer: (C) 10

Concept: Drop the altitude PM; in an equilateral triangle it bisects the base and equals $\frac{\sqrt{3}}{2}a$.

1. $QS=\frac{9}{3}=3$, $QM=4.5$ ⇒ $SM=1.5$
2. $P{M}^2=\frac{3}{4}\times 81=60.75$
3. $P{S}^2=P{M}^2+S{M}^2=60.75+2.25=63$
4. $PS=\sqrt{63}\text{cm}$

Trick: If $QS=\frac{a}{3}$ in an equilateral triangle, $P{S}^2=\frac{7}{9}{a}^2=\frac{7}{9}\times 81=63$.

Answer: (B) $\sqrt{63}$

Concept: $\text{CP}=\frac{\text{SP}}{1-\text{loss}\%}$; new SP $=\text{CP}\times (1+\text{gain}\%)$.

1. $\text{CP}=\frac{1596}{0.76}=$ ₹2,100
2. SP for 24% gain $=2100\times 1.24=$ ₹2,604

Trick: Directly: $1596\times \frac{124}{76}=21\times 124=2604$.

Answer: (D) 2604

Concept: $2n$ must be a common multiple of 12, 14, 16 and 18; least $2n$ = LCM.

1. $12=2^2\times 3$, $14=2\times 7$, $16=2^4$, $18=2\times 3^2$
2. $\text{LCM}=2^4\times 3^2\times 7=1008$
3. $n=\frac{1008}{2}=504$

Trick: Don't stop at the LCM (1008) – the question asks for the number that is doubled.

Answer: (C) 504

Concept: If $a:b=c:d$, the fourth proportional is $d=\frac{b\times c}{a}$.

1. $a=0.48,b=0.84,c=32$
2. $d=\frac{0.84\times 32}{0.48}$
3. $\frac{0.84}{0.48}=\frac{7}{4}$, so $d=\frac{7}{4}\times 32=56$

Trick: Remove decimals first: $0.84:0.48=84:48=7:4$.

Answer: (C) 56

Concept: Percentage less $=\frac{\text{Difference}}{\text{Base value}}\times 100$; base is the value being compared with (village P).

1. Illiterates in P $=380$, in R $=150$
2. Difference $=380-150=230$
3. $\frac{230}{380}\times 100=\frac{1150}{19}=60\frac{10}{19}\%$

Trick: Only the last column is needed; the ratio and literacy columns are distractors here.

Answer: (C) $60\frac{10}{19}\%$

Concept: Arc length $l=\frac{\theta }{{360}^{\circ }}\times 2\pi r$.

1. $r=42\text{cm},\theta ={60}^{\circ }$
2. $l=\frac{60}{360}\times 2\times \frac{22}{7}\times 42$
3. $=\frac{1}{6}\times 264=44\text{cm}$

Trick: ${60}^{\circ }$ is $\frac{1}{6}$ of the circle, so arc $=\frac{\text{circumference}}{6}=\frac{264}{6}$.

Answer: (A) $44\text{cm}$

Concept: $\text{Loss}\%=\frac{\text{CP}-\text{SP}}{\text{CP}}\times 100$.

1. CP $=625$, SP $=550$
2. Loss $=625-550=75$
3. $\text{Loss}\%=\frac{75}{625}\times 100=12\%$

Trick: $\frac{75}{625}=\frac{3}{25}=\frac{12}{100}$.

Answer: (A) $12\%$

Concept: Successive decreases: New value $=\text{Initial}\times (1-\frac{a}{100})(1-\frac{b}{100})$.

1. After year 1: $80000\times 0.95=76000$
2. After year 2: $76000\times 0.92=69920$

Trick: Net change $=-5-8+\frac{5\times 8}{100}=-12.6\%$; $80000\times 0.874=69920$.

Answer: (B) 69920

Concept: Average of two values $=\frac{\text{sum}}{2}$; then subtract.

1. Institute X (2010, 2011): $\frac{320+240}{2}=280$
2. Institute Y (2011, 2012): $\frac{320+200}{2}=260$
3. Difference $=280-260=20$

Trick: Difference of averages $=\frac{560-520}{2}=20$ — subtract the sums first.

Answer: (A) 20

Concept: Solid hemisphere: $\text{TSA}=3\pi r^2$, $V=\frac{2}{3}\pi r^3$.

1. $3\times \frac{22}{7}\times r^2=4158\Rightarrow r^2=441\Rightarrow r=21$
2. $V=\frac{2}{3}\times \frac{22}{7}\times {21}^3=\frac{2}{3}\times \frac{22}{7}\times 9261$
3. $V=19404{\text{cm}}^3$

Trick: $\frac{4158}{66}=63=3\times 21$ gives $\frac{r^2}{7}=63$, so $r=21$ quickly.

Answer: (D) 19404

Concept: Combined average $=\frac{\text{total weight}}{\text{total students}}$.

1. Totals: $8\times 48=384$, $4\times 44=176$, $4\times 58=232$
2. Sum $=384+176+232=792$
3. Average $=\frac{792}{16}=49.5\text{kg}$

Trick: Deviation from 48: $4\times (-4)+4\times (+10)=24$; $48+\frac{24}{16}=49.5$.

Answer: (A) $49.5\text{kg}$

Concept: $(a-b{)}^2-(a+b{)}^2=-4ab$.

1. Here $a=1,b=2x$
2. $(1-2x{)}^2-(1+2x{)}^2=-4\times 1\times 2x$
3. $=-8x$

Trick: Check with $x=1$: $(-1{)}^2-3^2=-8$, which matches $-8x$.

Answer: (B) $-8x$

Concept: Share from a ratio: part $=\frac{\text{ratio term}}{\text{sum of terms}}\times \text{total}$.

1. Seller A, Brand1 $=\frac{3}{4}\times 4000=3000$
2. Seller B, Brand2 $=\frac{1}{3}\times 6000=2000$
3. Difference $=3000-2000=1000$

Trick: Read carefully: Brand1 of A versus Brand2 of B.

Answer: (C) 1000