RRB ALP CBT 1 2025 PYQs

Concept: Equal amounts: $P_1(1.08{)}^{t_1}=P_2(1.08{)}^{t_2}$.

1. Mandar (15 yr) gets 8 years, Rupesh (14 yr) gets 9 years.
2. $M(1.08{)}^8=R(1.08{)}^9\Rightarrow M=1.08R$, i.e. $M:R=27:25$
3. $M=\frac{27}{52}\times 23400=12150$

Short trick: The one who has fewer years must get more money in the ratio $(1+r{)}^{\mathrm{\Delta }t}$ : 1 = 108 : 100 = 27 : 25.

Answer: (A) 12150

Concept: Know cubes up to 20 and fourth powers: ${17}^3=4913$, $6^4=1296$.

1. $\sqrt[3]{4913}=17$, $\sqrt[4]{1296}=6$
2. $\frac{17}{6}\times \frac{3}{51}\times 168=\frac{17\times 3\times 168}{6\times 51}$
3. $=\frac{1}{6}\times 168=28$ (since $17\times 3=51$)

Short trick: $\frac{17\times 3}{51}=1$ cancels at once, leaving $\frac{168}{6}=28$.

Answer: (B) 28

Concept: Profit is shared in the ratio of investments.

1. Total investment = 15600 + 10400 + 11700 = ₹37,700
2. Profit = 20% = ₹7,540; reinvested 5% = ₹377; distributed = ₹7,163
3. Ratio 15600 : 10400 : 11700 = 12 : 8 : 9 (sum 29)
4. Sunil = $\frac{9}{29}\times 7163=2223$

Short trick: Distributed profit = $0.2\times 0.95=19\mathrm{\%}$ of investment; Sunil’s share = 19% of his own ₹11,700 = ₹2,223.

Answer: (D) ₹2,223

Concept: $SI=\frac{P\times R\times T}{100}$

1. $480=\frac{P\times 16\times 2}{100}$
2. $P=\frac{48000}{32}=1500$

Short trick: Total rate = 16 × 2 = 32%; 32% = 480 ⇒ 1% = 15 ⇒ 100% = 1500.

Answer: (D) 1500

Concept: Arrange in ascending order; with 5 values the median is the 3rd.

1. $\frac{3}{7}\approx 0.43,\frac{3}{5}=0.6,\frac{11}{13}\approx 0.846,\frac{14}{16}=0.875,\frac{17}{19}\approx 0.895$
2. Middle (3rd) value $=\frac{11}{13}$

Short trick: For fractions $\frac{n}{n+2}$ (11/13, 14/16, 17/19) the value rises with $n$; 3/7 and 3/5 are clearly smaller, so the 3rd is $\frac{11}{13}$.

Answer: (B) $\frac{11}{13}$

Concept: Successive profits multiply.

1. Final SP = 1500 × 1.12 × 1.08
2. = 1680 × 1.08 = ₹1,814.40
3. Difference = 1814.40 − 1500 = ₹314.40

Short trick: Net profit % = 12 + 8 + (12×8)/100 = 20.96%; 20.96% of 1500 = ₹314.40.

Answer: (A) ₹314.40

Concept: Upstream speed $=8-s$, downstream speed $=8+s$.

1. $\frac{12}{8-s}+\frac{18}{8+s}=4$
2. $12(8+s)+18(8-s)=4(64-s^2)\Rightarrow 2s^2-3s-8=0$
3. $s=\frac{3+\sqrt{73}}{4}=\frac{3+8.544}{4}\approx 2.89$ km/hr

Short trick: Check options: $s=2.89$ gives $\frac{12}{5.11}+\frac{18}{10.89}=2.35+1.65=4.00$ h ✓.

Answer: (A) 2.89 km/hr

Concept: Change in average = (error in total) ÷ number of students.

1. Error in total = 99 − 35 = 64
2. $\frac{64}{n}=\frac{8}{3}\Rightarrow n=\frac{64\times 3}{8}=24$

Short trick: $n=\frac{\text{error}}{\text{change in average}}=64÷\frac{8}{3}=24$.

Answer: (D) 24

Concept: Multiply the growth factors.

1. 50000 × 1.25 = 62500
2. 62500 × 0.80 = 50000
3. 50000 × 1.10 = 55000

Short trick: +25% and −20% cancel exactly (5/4 × 4/5 = 1), so only +10% remains: 55,000.

Answer: (C) 55,000

Concept: Let CP = 100.

1. MP = 156, required SP = 117
2. Discount = 156 − 117 = 39
3. Discount % $=\frac{39}{156}\times 100=25\mathrm{\%}$

Short trick: $\frac{39}{156}=\frac{1}{4}$ since $156=4\times 39$ → 25%.

Answer: (D) 25%

Concept: Average speed = total distance ÷ total time.

1. Times: 60/30 = 2 h, 40/20 = 2 h, 50/25 = 2 h
2. Total distance = 150 km, total time = 6 h
3. Average = 150 ÷ 6 = 25 km/h

Short trick: Equal times on each part ⇒ average speed = simple mean of speeds = (30 + 20 + 25)/3 = 25.

Answer: (A) 25

Concept: Form the equation.

1. $\frac{x}{3}+83=97\Rightarrow \frac{x}{3}=14$
2. x = 42; sum of digits = 4 + 2 = 6

Short trick: (97 − 83) × 3 = 42 directly.

Answer: (C) 6

Concept: Let CP = x, so SP = 1.4x.

1. New CP = x + 28, new SP = 1.4x − 84
2. 1.4x − 84 = 1.375(x + 28) = 1.375x + 38.5
3. 0.025x = 122.5 ⇒ x = 4900

Short trick: Check option A: SP = 6860; new SP 6776, new CP 4928; 4928 × 1.375 = 6776 ✓.

Answer: (A) 4,900

Concept: Mode is the most frequent value.

1. Count the option values only: 60 → 2 times, 61 → 3 times, 77 → 2 times, 78 → 4 times.
2. Highest frequency = 4 ⇒ mode = 78.

Short trick: Count only the four option values instead of tallying all 25 numbers.

Answer: (B) 78

Concept: In a right triangle, the altitude to the hypotenuse is the mean proportional of the two segments: $B{D}^2=AD\times DC$.

1. $B{D}^2=5\times 9=45$
2. $BD=\sqrt{45}=3\sqrt{5}$ cm

Short trick: Altitude = $\sqrt{\text{product of segments}}$ — same as "mean proportional".

Answer: (C) $3\sqrt{5}$

Concept: Use LCM as total work.

1. Total work = LCM(15, 20) = 60 units
2. A = 4 units/day, B = 3 units/day; together 7
3. Time $=\frac{60}{7}=8\frac{4}{7}$ days

Short trick: Together time = $\frac{ab}{a+b}=\frac{15\times 20}{35}=\frac{60}{7}$.

Answer: (D) $8\frac{4}{7}$ days

Concept: A quantity compared with itself is always 100%.

1. 5% of N ÷ 5% of N = 1
2. 1 × 100 = 100%

Short trick: Same quantity on both sides ⇒ 100%, no calculation needed.

Answer: (C) 100%

Concept: Let CP = 100.

1. MP = 130; SP = 130 × 0.8 = 104 ⇒ profit 4%
2. 4% of CP = ₹32 ⇒ CP = 32 × 25 = ₹800

Short trick: Net effect of +30% then −20% = 30 − 20 − 6 = +4%; 4% = 32 ⇒ 100% = 800.

Answer: (D) 800

Concept: Profit ratio = capital × time.

1. Tarun : Varun = 12000 × 4 : 72000 × 10 = 48 : 720 = 1 : 15
2. Total profit = 16800 ÷ 0.20 = ₹84,000
3. Varun = $\frac{15}{16}\times 84000=78750$

Short trick: Varun = total − Tarun = 84000 − 84000/16 = 84000 − 5250 = 78,750.

Answer: (A) 78,750

Concept: Curved surface area of a hemisphere $=2\pi r^2$.

1. $2\pi \times {125}^2=2\pi \times 15625$
2. $=31250\pi$ cm²

Short trick: ${125}^2=15625$ (since $5^6$); double it → $31250\pi$. Only option ending in 0.

Answer: (A) $31250\pi$