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

Concept: Do × and ÷ left to right, then addition.

1. $\frac{1}{4}\times \frac{4}{3}=\frac{1}{3}$
2. $\frac{1}{3}÷\frac{5}{3}=\frac{1}{3}\times \frac{3}{5}=\frac{1}{5}$
3. $\frac{1}{5}+\frac{1}{2}=\frac{7}{10}=0.7$

Trick: Division by a fraction = multiply by its reciprocal.

Answer: (A) $0.7$

Concept: Females below poverty line = population × BPL% × female share of the BPL ratio.

1. State A: BPL $=36\%$ of $18000=6480$; females $=\frac{3}{8}\times 6480=2430$
2. State D: BPL $=32\%$ of $18000=5760$; females $=\frac{2}{3}\times 5760=3840$
3. Total $=2430+3840=6270$

Trick: Use only the 'Below poverty line' ratio column; the 'Above' column is a trap.

Answer: (B) $6270$

Concept: Aarav's gain = money received on selling − money paid to buy it back, measured on the original worth.

1. Aarav sells at $10000\times 1.15=₹11500$
2. Bhavin sells back at $11500\times 0.85=₹9775$
3. Gain $=11500-9775=₹1725$; $\frac{1725}{10000}\times 100=17.25\%$ profit

Trick: He gets the watch back and keeps the difference: $11500\times 15\%=1725$, i.e. $1.15\times 15=17.25\%$.

Answer: (D) 17.25% profit

Concept: Successive changes multiply: increase → ×1.15, decrease → ×0.85.

1. 2012 increase, 2013 decrease, 2014 increase (three changes by the start of 2015).
2. Factor $=1.15\times 0.85\times 1.15=0.9775\times 1.15=1.124125$
3. Change $=+12.41\%$ (increase)

Trick: $+15$ and $-15$ give $-2.25\%$; then $-2.25+15-\frac{2.25\times 15}{100}=12.41\%$.

Answer: (B) Increased by 12.41 %

Concept: Division and multiplication left to right first, then addition and subtraction.

1. $180÷30\times 6=6\times 6=36$; $60÷3=20$
2. $30+36-15-16-20-15$
3. $=66-66=0$

Trick: Add all positives ($66$) and all negatives ($66$) separately.

Answer: (C) $0$

Concept: Convert mixed fractions to improper fractions and solve the innermost bracket first.

1. $3\frac{3}{5}÷4\frac{1}{2}=\frac{18}{5}\times \frac{2}{9}=\frac{4}{5}$; $5\frac{1}{4}\times \frac{4}{5}=\frac{21}{5}$
2. $1\frac{3}{4}÷\frac{21}{5}=\frac{7}{4}\times \frac{5}{21}=\frac{5}{12}$; $3\frac{2}{3}÷\frac{5}{12}=\frac{11}{3}\times \frac{12}{5}=\frac{44}{5}$
3. Numerator $=12+\frac{44}{5}=\frac{104}{5}$; denominator $=\frac{4}{3}\times \frac{26}{5}=\frac{104}{15}$
4. Value $=\frac{104}{5}\times \frac{15}{104}=3$

Trick: Same $104$ in numerator and denominator – a sign the answer is a neat integer.

Answer: (B) $3$

Concept: Count the subjects (columns) in which at least one student scored 100.

1. Math: A and C scored 100 ✓
2. Chemistry: A scored 100 ✓
3. Information Technology: A and C scored 100 ✓
4. English and Physics: no 100 → $3$ subjects.

Trick: The question counts subjects, not the number of 100s (which is 5).

Answer: (C) $3$

Concept: Total = average × number; divide the total in the given ratio.

1. Total age $=25\times 3=75$ years
2. Ratio sum $=3+5+7=15$
3. Youngest $=\frac{3}{15}\times 75=15$ years

Trick: One part $=\frac{75}{15}=5$; youngest $=3\times 5$.

Answer: (C) 15 years

Concept: Amounts are proportional to the central angles.

1. Savings ${60}^{\circ }=₹8000$
2. Education ${30}^{\circ }=\frac{30}{60}\times 8000=₹4000$

Trick: Education angle is half of savings angle → half the amount.

Answer: (B) $4000$

Concept: $a^2+b^2+c^2+2ab+2bc+2ca=(a+b+c{)}^2$.

1. Here $a=25,b=9,c=6$
2. Value $=(25+9+6{)}^2={40}^2=1600$

Yaad rakhein: Three squares + all doubled cross-products = square of the sum.

Answer: (C) $1600$

Concept: Brackets first (inner to outer), then ×, then +.

1. $(5+7)=12$; $12÷2=6$
2. $[7+6]=13$
3. $3+2\times 13=3+26=29$

Trick: Never add $3+2$ first – multiplication comes before addition.

Answer: (A) $29$

Concept: Central angle $=\frac{\text{percentage}}{100}\times {360}^{\circ }$.

1. Store S $=34\%$
2. Angle $=\frac{34}{100}\times {360}^{\circ }={122.4}^{\circ }$

Trick: $1\%={3.6}^{\circ }$, so $34\%=34\times 3.6={122.4}^{\circ }$ (total 6500 not needed).

Answer: (B) ${122.4}^{\circ }$

Concept: Under SI, each instalment earns interest from its payment date till the due date; total must equal the debt due.

1. Let instalment $=x$. 1st earns 2 years: $x(1+0.2)=1.2x$
2. 2nd earns 1 year: $1.1x$; 3rd earns none: $x$
3. $1.2x+1.1x+x=3.3x=10192\Rightarrow x=\frac{10192}{3.3}=3088.48$

Trick: Formula: $x=\frac{100A}{100n+\frac{n(n-1)}{2}R}=\frac{1019200}{300+30}$.

Answer: (B) ₹3,088.48

Concept: Cube volume $a^3$, TSA $6a^2$; cuboid volume $lbh$, TSA $2(lb+bh+hl)$.

1. Cuboid volume $=32\times 8\times 4=1024$; cube volume $=4\times 1024=4096\Rightarrow a=16$
2. Cube TSA $=6\times {16}^2=1536$
3. Cuboid TSA $=2(256+32+128)=832$
4. Ratio $=1536:832=24:13$

Trick: Divide both by $64$: $1536÷64=24$, $832÷64=13$.

Answer: (A) 24 : 13

Concept: BODMAS: ÷ and × left to right before + and −.

1. $4.5÷0.9=5$; $5\times 1.2=6$
2. $8.2+2.6+3.2=14$
3. $14-6=8$

Trick: $4.5÷0.9$ is the same as $45÷9$.

Answer: (D) $8$

Concept: A median divides a triangle into two triangles of equal area (equal bases, same height).

1. XL is a median since L is the mid-point of YZ.
2. Area $△XYL=$ Area $△XLZ=13{\text{cm}}^2$
3. Area $△XYZ=2\times 13=26{\text{cm}}^2$

Yaad rakhein: Median → two equal halves.

Answer: (D) $26$

Concept: Difference of times for the same distance: $\frac{d}{s_1}-\frac{d}{s_2}=\Delta t$.

1. $40$ min $=\frac{2}{3}$ h
2. $\frac{d}{45}-\frac{d}{55}=\frac{2}{3}\Rightarrow d·\frac{10}{2475}=\frac{2}{3}$
3. $d=\frac{2\times 2475}{30}=165\text{km}$

Trick: $d=\frac{s_1{s}_2}{s_2-s_1}\times \Delta t=\frac{45\times 55}{10}\times \frac{2}{3}=165$.

Answer: (B) $165$

Concept: Each decrease multiplies the remaining population: $P\times 0.95\times 0.80$.

1. $P\times 0.95\times 0.8=0.76P$
2. $0.76P=4655\Rightarrow P=\frac{4655}{0.76}=6125$

Trick: Check options backwards: $6125\times 0.95=5818.75$, $\times 0.8=4655$ ✓.

Answer: (B) $6125$

Concept: Square and add the two given equations; use ${\sin }^2+{\cos }^2=1$.

1. $a^2={\sin }^{2}x+{\sin }^{2}y+2\sin x\sin y$
2. $b^2={\cos }^{2}x+{\cos }^{2}y+2\cos x\cos y$
3. $a^2+b^2=2+2(\sin x\sin y+\cos x\cos y)$
4. $\sin x\sin y+\cos x\cos y=\frac{a^2+b^2-2}{2}$

Trick: Put $x=y=0$: $a=0,b=2$ → value $1=\frac{0+4-2}{2}$ ✓.

Answer: (C) $\frac{a^2+b^2-2}{2}$

Concept: Apply the first discount on the marked price, then find the second discount on the reduced price.

1. After 10%: $2500\times 0.9=₹2250$
2. Second discount $=2250-1800=₹450$
3. Rate $=\frac{450}{2250}\times 100=20\%$

Trick: $\frac{1800}{2500}=0.72=0.9\times 0.8$ → second discount 20%.

Answer: (B) 20%