SSC CHSL 2025 PYQs

Concept: Amount = 184% ⇒ SI = 84% of P in 6 years.

1. Rate = $84÷6=14\%$ p.a.
2. SI on 3500 for 3 years = $\frac{3500\times 14\times 3}{100}$
3. = ₹1470

Trick: 3 years at 14% = 42% of 3500 = 1470.

Answer: (D) Rs. 1470

Concept: Let shares be 4x and 5x; equate the interest difference.

1. Kavya: $4x\times 8\times \frac{5}{100}=1.6x$; Aryan: $5x\times 7\times \frac{5}{100}=1.75x$
2. $0.15x=2691\Rightarrow x=17940$
3. Distributed = $9x=161460$ = 90% of total
4. Total = $161460\times \frac{10}{9}=$ ₹1,79,400

Trick: Total = $2691÷0.15\times 9÷0.9=2691\times 60$ = 1,61,460 ÷ 0.9 – or check: 90% of 1,79,400 = 1,61,460 ✔

Answer: (B) Rs. 1,79,400

Concept: $\tan \theta =\frac{\text{height}}{\text{base}}$; use the Pythagorean triplet.

1. $\tan \theta =\frac{8}{15}$ ⇒ $\text{height}=8k,\text{base}=15k$
2. $\text{Ladder}=\sqrt{64+225}k=17k$
3. $17k=17\Rightarrow k=1\Rightarrow$ height = 8 m

Trick: 8-15-17 is a Pythagorean triplet – ladder already 17, so height is simply 8.

Answer: (C) 8 meters

Concept: Under CI, equal time blocks multiply money by the same factor.

1. 6-year factor = $\frac{9000}{4000}=\frac{9}{4}$
2. 3-year factor = $\sqrt{\frac{9}{4}}=\frac{3}{2}$
3. Amount = $3200\times \frac{3}{2}=$ ₹4,800

Trick: Half the time ⇒ square root of the growth factor.

Answer: (B) Rs. 4,800

Concept: Present ages 3x and 7x; after 6 years ratio is 3 : 5.

1. $\frac{3x+6}{7x+6}=\frac{3}{5}$
2. $15x+30=21x+18\Rightarrow x=2$
3. Son = 6, mother = 14

Trick: Test options: 6 : 14 = 3 : 7 and 12 : 20 = 3 : 5 ✔ – done.

Answer: (A) 6,14

Concept: Tangent–chord angle = inscribed angle in the alternate segment; centre angle = 2 × inscribed angle.

1. Angle between tangent at A and chord AC = 50° ⇒ inscribed angle on arc AC = 50°.
2. Angle at centre by minor arc AC = $2\times {50}^{\circ }=$ 100°.
3. The 85° (on chord AB) is extra data.

Trick: Tangent–chord angle × 2 = central angle of that chord, directly.

Answer: (C) 100°

Concept: For the same distance, time is inversely proportional to speed.

1. Train time = 6 h
2. Speed ratio 8 : 3 ⇒ time ratio 3 : 8
3. Car time = $6\times \frac{8}{3}=$ 16 hours

Trick: Same distance: ${\text{time}}_2={\text{time}}_1\times \frac{{\text{speed}}_1}{{\text{speed}}_2}$.

Answer: (B) 16 hours

Concept: Passed = $(100-\text{fail})\%$ of each group.

1. Boys passed = 70% of 5 = 3.5
2. Girls passed = 50% of 7 = 3.5
3. Ratio = 3.5 : 3.5 = 1 : 1

Trick: Directly: $5\times 70:7\times 50=350:350$.

Answer: (C) 1 : 1

Concept: sec A = cosec B ⇒ A + B = 90°.

1. sec θ = cosec 52°
2. θ + 52° = 90°
3. θ = 38°

Trick: Co-function pairs (sin–cos, tan–cot, sec–cosec) with equal values ⇒ angles add to 90°.

Answer: (B) 38°

Concept: Write everything as a power of 5 and compare exponents.

1. $(\sqrt{5}{)}^6=5^3;{25}^2=5^4\Rightarrow \text{LHS}=5^7$
2. $\text{RHS}=5^n\times 5\sqrt{5}=5^{n+\frac{3}{2}}$
3. $n+\frac{3}{2}=7\Rightarrow n=$ $\frac{11}{2}$

Trick: $\sqrt{5}=5^{\frac{1}{2}}$, so $5\sqrt{5}=5^{\frac{3}{2}}$ – convert roots to half-powers first.

Answer: (C) $\frac{11}{2}$

Concept: For $y=a-\sqrt{b}$ with $a^2-b=1$, $\frac{1}{y}=a+\sqrt{b}$.

1. $y=5-\sqrt{24};(5{)}^2-24=1$
2. $\frac{1}{y}=5+\sqrt{24}$
3. $y+\frac{1}{y}=$ 10

Trick: When $a^2-b=1$, $y+\frac{1}{y}=2a$ straight away ($2\times 5=10$).

Answer: (C) 10

Concept: Area ratio = $(\text{side ratio}{)}^2$.

1. Area ratio = $48:6=8$
2. Side ratio = $\sqrt{8}=2\sqrt{2}$
3. Larger side = $3\times 2\sqrt{2}=$ $6\sqrt{2}$ cm

Trick: $\text{Side scale}=\sqrt{\text{area scale}}$ – never multiply the side by 8.

Answer: (B) $6\sqrt{2}\mathrm{cm}$

Concept: Area of similar figures $\propto (\text{height}{)}^2$.

1. Height ratio 1 : 4 ⇒ area ratio 1 : 16
2. Trapezium = $16-1=15$ parts
3. Trapezium : large triangle = 15 : 16

Trick: Ratio k ⇒ remaining part : whole = $(1-k^2):1=\frac{15}{16}$.

Answer: (B) $15:16$

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

1. $={12}^2-2\times 14$
2. $=144-28=$ 116

Yaad rakhein: Similarly $(a-b{)}^2=(a+b{)}^2-4ab=144-56=88$.

Answer: (D) 116

Concept: $\frac{x^3+y^3}{x+y}=x^2-xy+y^2$.

1. $x=\frac{16+8}{2}=12,y=4$
2. $x^2-xy+y^2=144-48+16$
3. = 112

Trick: $x^2-xy+y^2=\frac{(x+y{)}^2+3(x-y{)}^2}{4}=\frac{256+192}{4}=112$.

Answer: (C) 112

Concept: For n5, $(n5{)}^2=n\times (n+1)$ followed by 25.

1. 175 → $n=17$, $n+1=18$.
2. $17\times 18=306$.
3. Write 25 after it → ${175}^2=30625$.

Trick: Units digit of the square must be 25 and ${175}^2<{180}^2=32400$ → only 30625 fits.

Answer: (A) 30625

Concept: Substitute standard trigonometric values.

1. $\cos {45}^{\circ }\times \sin {45}^{\circ }=\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)=\frac{1}{2}$.
2. $\cot {60}^{\circ }\times \csc {30}^{\circ }=\frac{1}{\sqrt{3}}\times 2=\frac{2}{\sqrt{3}}$.
3. $\sec {30}^{\circ }\times \tan {45}^{\circ }=\frac{2}{\sqrt{3}}\times 1=\frac{2}{\sqrt{3}}$.
4. Sum = $\frac{1}{2}+\frac{4}{\sqrt{3}}$.

Trick: Notice the last two terms are both $\frac{2}{\sqrt{3}}$ – just double it.

Answer: (B) $\left(\frac{1}{2}+\frac{4}{\sqrt{3}}\right)$

Concept: Use tan in the right triangles formed from the hilltop.

1. Foot of pole at 60°: $\tan {60}^{\circ }=\frac{300}{d}\to d=\frac{300}{\sqrt{3}}=100\sqrt{3}$ m.
2. Top of pole at 30°: $\tan {30}^{\circ }=\frac{300-h}{d}\to 300-h=100\sqrt{3}\times \frac{1}{\sqrt{3}}=100\to h=200$ m.
3. $h-d=200-100\sqrt{3}=100(2-\sqrt{3})$ m.

Trick: With 60° and 30° from the same point, the vertical drops are in ratio 3 : 1 → $300-h=100$ directly.

Answer: (D) $100\left(2-\sqrt{3}\right)$

Concept: Water overflow = volume of the solid immersed.

1. Sphere diameter = 12 cm = cube side, so it fits fully.
2. Volume = $\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times 216=288\pi {\text{cm}}^3$.

Trick: Don't subtract from the cube volume – overflow equals the sphere's volume itself.

Answer: (A) $288\pi$

Concept: In a right triangle the median to the hypotenuse = half the hypotenuse.

1. Check: ${85}^2+{120}^2=7225+14400=21625={145}^2$ → right angle at B.
2. M is the midpoint of hypotenuse CA.
3. $BM=\frac{145}{2}=72.5$ cm.

Trick: 85 : 120 : 145 = 17 : 24 : 29 (×5) – a known triplet, so spot the right angle instantly.

Answer: (B) 72.5 cm