SSC CHSL 2025 PYQs

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

1. Expression = $(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})$.
2. $=(\sqrt{3}{)}^2-(\sqrt{2}{)}^2=3-2=1$.

Trick: Conjugate surds always multiply to a rational number: just subtract the numbers under the roots.

Answer: (B) 1

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

1. $a+b=(2+\sqrt{5})+(2-\sqrt{5})=4$.
2. $ab=2^2-(\sqrt{5}{)}^2=4-5=-1$.
3. $a^2+b^2=16-2(-1)=18$.

Trick: For $a=p+\sqrt{q},b=p-\sqrt{q}$: $a^2+b^2=2(p^2+q)=2(4+5)=18$.

Answer: (D) 18

Concept: $\text{Profit ratio}=\text{capital}\times \text{months}$.

1. P: $14000\times 12=1,68,000$.
2. Q: $20000\times 3=60,000$.
3. Ratio = 168 : 60 = 14 : 5.

Trick: Cut zeros first: $14\times 12:20\times 3=168:60$ → ÷12 → 14 : 5.

Answer: (B) 14 : 5

Concept: Let ages be 5x and 7x; after 6 years ratio 7 : 9.

1. Cross-multiplying: $49x+42=45x+54$.
2. $4x=12\to x=3$.
3. $P=5x=15$ years.

Trick: Difference stays same: 7−5 = 2 parts and 9−7 = 2 parts, so $7-5=2$ parts = 6 → 1 part = 3; P = $5\times 3=15$.

Answer: (B) 15

Concept: $\text{Average}=\text{sum}÷\text{count}$.

1. $(4+6+8)÷3=18÷3=6$.
2. New average = $6+4=10$.

Trick: For equally spaced numbers the average is the middle number (6).

Answer: (C) 10

Concept: $\%\text{ change}=\frac{\text{change}}{\text{original}}\times 100$.

1. Change = $300-250=50$.
2. % decrease = $\frac{50}{300}\times 100=16.67\%$.

Trick: $\frac{50}{300}=\frac{1}{6}$ and $\frac{1}{6}=16.67\%$ – learn fraction-percent equivalents.

Answer: (D) $16.67\%$

Concept: If A is r% less than B, then B is more than A by $\frac{r}{100-r}\times 100\%$.

1. Q = 100, P = 70.
2. Q more than P = $\frac{30}{70}\times 100=42.85\%$.

Trick: $\frac{30}{100-30}=\frac{3}{7}\approx 42.85\%$ – one-step formula.

Answer: (C) $42.85\%$

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

1. $\text{SP}=1200\times \frac{85}{100}$.
2. $=12\times 85=$ ₹1,020.

Trick: 15% of 1200 = 180; $1200-180=1020$.

Answer: (C) ₹1020

Concept: Same SP, x% gain on one and x% loss on other ⇒ always a loss of $\frac{x^2}{100}\%$.

1. $x=25$ → loss = $\frac{625}{100}=6.25\%$.
2. Check: ${\text{CP}}_1=800\times \frac{100}{125}=640$, ${\text{CP}}_2=800\times \frac{100}{75}\approx 1066.67$; total $\text{CP}\approx 1706.67>\text{SP}1600$ → loss.

Trick: Equal SP + equal % → loss, never gain: ${\left(\frac{x}{10}\right)}^2\%=(2.5{)}^2=6.25\%$.

Answer: (A) 6.25% loss

Concept: $\text{Discount}\%=\frac{\text{MP}-\text{SP}}{\text{MP}}\times 100$.

1. Discount = $1800-1260=540$.
2. $\frac{540}{1800}\times 100=30\%$.

Trick: $\frac{\text{SP}}{\text{MP}}=\frac{1260}{1800}=0.7$ → 70% paid → 30% discount.

Answer: (B) 30%

Concept: When only juice is added, water stays constant.

1. Juice = $\frac{5}{8}\times 64=40$ L, water = $\frac{3}{8}\times 64=24$ L.
2. New ratio 7 : 1 → juice = $7\times 24=168$ L.
3. Juice to add = $168-40=128$ L.

Trick: Keep the unchanged part fixed: water 3 parts = 24 → make water '1 part' = 24, juice $7\times 24$.

Answer: (D) 128 L

Concept: Cylinder = $\pi r^{2}h$; cone = $\frac{1}{3}\pi r^{2}h$.

1. Same r and h → ratio = $1:\frac{1}{3}$.
2. = 3 : 1.

Yaad rakhein: Three cones of the same base and height fill one cylinder.

Answer: (B) (3 : 1)

Concept: Sum of interior angles = (n − 2) × 180°.

1. Hexagon: n = 6.
2. (6 − 2) × 180° = 720°.
3. The surrounding circle is extra information – ignore it.

Trick: Each extra side adds 180°: triangle 180°, quadrilateral 360°, pentagon 540°, hexagon 720°.

Answer: (B) ${720}^{\circ }$

Concept: Each interior angle = ${180}^{\circ }-\frac{{360}^{\circ }}{n}$.

1. Exterior angle = $\frac{{360}^{\circ }}{8}={45}^{\circ }$.
2. Interior = ${180}^{\circ }-{45}^{\circ }={135}^{\circ }$.

Trick: Exterior first $(360÷n)$, then subtract from 180 – faster than $\frac{(n-2)\times 180}{n}$.

Answer: (A) 135°

Concept: Volume is conserved: $\text{number}=\text{big volume}÷\text{small volume}$.

1. Cylinder = $\pi \times 4^2\times 21=336\pi {\text{cm}}^3$.
2. Hemisphere = $\frac{2}{3}\pi \times 2^3=\frac{16\pi }{3}{\text{cm}}^3$.
3. Number = $336\pi ÷\left(\frac{16\pi }{3}\right)=336\times \frac{3}{16}=63$.

Trick: Cancel π at once and keep numbers as factors: $\frac{16\times 21\times 3}{2\times 8}=63$.

Answer: (C) 63

Concept: Lateral (curved) surface of a cylinder = $2\pi rh$.

1. $r=10$ cm, $h=18$ cm.
2. $2\pi \times 10\times 18=360\pi {\text{cm}}^2$.

Yaad rakhein: 'Lateral/curved' = $2\pi rh$; 'total' adds $2\pi r^2$ for the two ends.

Answer: (B) $360\pi {\mathrm{cm}}^2$

Concept: 5, 12, 13 is a Pythagorean triple → right triangle with legs 5 and 12.

1. One triangular face = $\frac{1}{2}\times 5\times 12=30{\text{cm}}^2$.
2. Three rectangles = $\text{perimeter}\times \text{length}=(5+12+13)\times 10=300{\text{cm}}^2$.
3. Total = $30+300=330{\text{cm}}^2$.

Trick: Lateral area of any prism = $\text{base perimeter}\times \text{length}$.

Answer: (D) $330{\mathrm{cm}}^2$

Concept: Volume of hemisphere = $\frac{2}{3}\pi r^3$.

1. $\frac{2}{3}\pi r^3=144\pi \to r^3=144\times \frac{3}{2}=216$.
2. $r=\sqrt[3]{216}=6$ m.

Trick: Option check: $\frac{2}{3}\times 6^3=144$ ✔ – plug options when the formula is simple.

Answer: (A) 6 m

Concept: For a.bcbc…: fraction = $\frac{abc-a}{99}$.

1. 7.1818… → $\frac{718-7}{99}=\frac{711}{99}$.
2. Divide by 9: $\frac{711}{99}=\frac{79}{11}$.

Trick: Check: $79÷11=7.1818\dots$ ✔ (any $\frac{n}{11}$ gives a repeating 2-digit block).

Answer: (C) $\frac{79}{11}$

Concept: $\cos ({90}^{\circ }-\theta )=\sin \theta$.

1. So $\sin \theta \times \cos ({90}^{\circ }-\theta )={\sin }^2\theta$.
2. $\tan \theta =\frac{3}{4}$ → 3-4-5 triangle → $\sin \theta =\frac{3}{5}$.
3. ${\sin }^2\theta =\frac{9}{25}$.

Trick: ${\sin }^2\theta =\frac{{\tan }^2\theta }{1+{\tan }^2\theta }=\frac{9/16}{25/16}=\frac{9}{25}$.

Answer: (B) $\frac{9}{25}$