SSC CHSL 2025 PYQs

Concept: Find the smallest and largest n with $30<n^2<900$.

1. $6^2=36$ (first), ${29}^2=841$ (last; ${30}^2=900$ is excluded).
2. Count = $29-6+1=24$.

Trick: $\sqrt{30}\approx 5.5$ and $\sqrt{900}=30$ → n runs from 6 to 29.

Answer: (C) 24

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

1. $\text{SI}=\frac{8000\times 5\times 4}{100}=$ ₹1,600.
2. Amount = $8000+1600=$ ₹9,600.

Trick: $R\times T=20\%$ → Amount = 120% of 8000 = 9600.

Answer: (A) ₹9,600

Concept: $a^3+b^3=(a+b)(a^2-ab+b^2)$.

1. Expression = $\frac{a^3+b^3}{a^2-ab+b^2}$ with $a=545$, $b=315$.
2. $=a+b=545+315=860$.

Trick: Numerator $a^3+b^3$, denominator $a^2-ab+b^2$ → answer $a+b$; with $a^3-b^3$ and $a^2+ab+b^2$ → $a-b$.

Answer: (A) 860

Concept: $1+2+\dots +n+\dots +2+1=n^2$.

1. Peak $n=31$.
2. Sum = ${31}^2=961$.

Trick: Check: $2\times \left(\frac{30\times 31}{2}\right)+31=930+31=961$ ✔.

Answer: (B) 961

Concept: $\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$.

1. $\frac{1+\sin x}{\cos x}=\frac{1}{\cos x}+\frac{\sin x}{\cos x}$.
2. $=\sec x+\tan x$.

Trick: $\frac{1}{\cos }=\sec$, $\frac{\sin }{\cos }=\tan$; $\cot$ is $\frac{\cos }{\sin }$, so (A) is wrong.

Answer: (B) $\sec \left(x\right)+\tan \left(x\right)$

Concept: Profit is divided in the ratio of $(\text{money}\times \text{months})$.

1. A = $6000\times 10=60000$, B = $4000\times 8=32000$, C = $5000\times 8=40000$
2. Ratio = 15 : 8 : 10 (÷ 4000); total 33 parts
3. 1 part = $330000÷33=$ ₹10,000
4. B = $8\times 10000=$ ₹80,000

Trick: ₹$3,30,000÷33=10,000$ is clean – a sign the ratio is right.

Answer: (B) ₹80,000

Concept: Use $(a+b{)}^2=a^2+b^2+2ab$ and $a^3+b^3=(a+b)(a^2+b^2-ab)$.

1. $225=117+2ab\to ab=54$
2. $a^3+b^3=15\times (117-54)$
3. $=15\times 63=945$

Trick: Guess numbers: $a+b=15,ab=54\to a=9,b=6$; $729+216=945$.

Answer: (D) 945

Concept: $\text{Total}=\text{students}\times \text{candies each}$: $R(R+6)=432$.

1. $R^2+6R-432=0$
2. $(R+24)(R-18)=0$
3. $R=18$ (students cannot be negative)

Trick: Check options: $18\times 24=432$ ✓ – no equation needed.

Answer: (D) 18

Concept: $\text{Volume of cone}=\frac{1}{3}\pi r^{2}h$.

1. $\frac{1}{3}\times \frac{22}{7}\times r^2\times 9=4158$
2. $\frac{66}{7}{r}^2=4158$
3. $r^2=4158\times \frac{7}{66}=441$
4. $r=21$ cm

Trick: Volume has $\frac{22}{7}$ → r is usually a multiple of 7; only 21 fits.

Answer: (C) 21 cm

Concept: $\text{Exterior angle}=\frac{{360}^{\circ }}{n}$ and $\text{interior}={180}^{\circ }-\text{exterior}$.

1. Smaller: $\text{exterior}={180}^{\circ }-{150}^{\circ }={30}^{\circ }\to n=\frac{360}{30}=12$
2. Larger: $3\times 12=36$ sides
3. $\text{Exterior}=\frac{360}{36}={10}^{\circ }\to \text{interior}={170}^{\circ }$

Trick: Perimeter and side ratio are distractors – angle depends only on number of sides.

Answer: (B) 170*

Concept: Show $△ABD\cong △ACE$, then equate matching sides.

1. $AD=AE\to \angle ADE=\angle AED\to$ their supplements $\angle ADB=\angle AEC$.
2. With $\angle BAD=\angle CAE$ and $AD=AE\to △ABD\cong △ACE$ (ASA).
3. So $BD=CE\to 3p=q$, and $AB=AC\to 2p+4=3q-8$.
4. $2p+4=9p-8\to p=\frac{12}{7},q=\frac{36}{7}\to p+q=\frac{48}{7}$.

Trick: Once you see $BD=CE$, write $q=3p$ and substitute – one-variable equation.

Answer: (B) $\frac{48}{7}$

Concept: A cuboid has 12 edges: total = $4(l+b+h)$.

1. $l+b+h=280÷4=70$
2. $3x+5x+6x=14x=70\to x=5$
3. $l=15,b=25,h=30$
4. Volume = $15\times 25\times 30=11250{\text{cm}}^3$

Trick: $\text{Volume}=90x^3=90\times 125=11250$.

Answer: (B) 11250 cubic cm

Concept: Volume stays the same after melting.

1. $n=\frac{4}{3}\pi (21{)}^3÷\frac{2}{3}\pi (7{)}^3=2\times 3^3=54$
2. $\text{CSA of one hemisphere}=2\pi r^2=2\pi \times 49=98\pi$
3. Total = $54\times 98\pi =5292\pi {\text{cm}}^2$

Trick: Radius ratio 3:1 → sphere = 27 small spheres = 54 hemispheres.

Answer: (B) $5292\pi {\mathrm{cm}}^2$

Concept: $\text{LSA}=\frac{1}{2}\times \text{perimeter of base}\times \text{slant height}$.

1. Base perimeter $=4\times 11.5=46$ m
2. $\text{LSA}=\frac{1}{2}\times 46\times 20=460{\text{m}}^2$

Trick: Half the perimeter (23) × slant height (20) = 460 – one-step mental calculation.

Answer: (C) $460m^2$

Concept: Break-even: profit amount = loss amount.

1. $20\%{\text{ of CP}}_1=30\%{\text{ of CP}}_2$
2. $\frac{{\text{CP}}_1}{{\text{CP}}_2}=\frac{30}{20}=\frac{3}{2}$

Trick: Ratio of CPs = inverse of the percentages: 20 : 30 → 3 : 2.

Answer: (C) $\mathrm{CP}=3:2$

Concept: Same time period → profit ratio = investment ratio.

1. 7 parts = ₹70,000 → 1 part = ₹10,000
2. B = 8 parts = ₹80,000

Trick: 7 → 70,000 means multiply by 10,000; 8 → 80,000.

Answer: (B) Rs 80,000

Concept: Make the common term Q equal in both ratios.

1. P : Q = 3 : 5 = 6 : 10; Q : R = 2 : 3 = 10 : 15
2. P : Q : R = 6 : 10 : 15 → 31 parts
3. 1 part = $6200÷31=200$ → Q = 2000

Trick: $6200÷31=200$ exactly – confirms the combined ratio.

Answer: (B) 2000

Concept: Equal total work: $(\text{workers}\times \text{days})$ is the same for both groups.

1. $\text{Group 1}\times 12\text{ days}=\text{Group 2}\times 4\text{ days}$ → $3(6M+5B)=15M+20B$
2. $18M+15B=15M+20B\to 3M=5B\to M:B=5:3$
3. Work = $12(30+15)=540$ units
4. $9M+15B=45+45=90$ units/day → $540÷90=6$ days

Trick: Take 1 man = 5, 1 boy = 3 units – everything becomes whole numbers.

Answer: (D) 6 days

Concept: Marked price is fixed; $\text{SP}=(100-d)\%$ of MP.

1. 82% of MP = 8364 → $\text{MP}=8364\times \frac{100}{82}=10200$
2. SP at 30% off = 70% of 10200 = ₹7,140

Trick: Direct: $8364\times \frac{70}{82}=102\times 70=7140$.

Answer: (B) ₹7,140

Concept: Under SI, time is proportional to interest earned.

1. 7 times → interest = 6P in 18 years
2. 10 times → interest = 9P
3. Time = $18\times \frac{9}{6}=27$ years

Trick: $T_2=T_1\times \frac{n_2-1}{n_1-1}=18\times \frac{9}{6}=27$.

Answer: (B) 27 years