RRB ALP CBT 1 2025 PYQs

Concept: Find MP from the discounted price, then CP from the profit on MP.

1. After 90% and 50% discounts, SP = MP × 0.1 × 0.5 = 0.05 MP.
2. 0.05 MP = 225.6 → MP = 4512.
3. MP gives 41% profit: CP = 4512 ÷ 1.41 = 3200.

Short trick: $225.6\times 20=4512$, and 3200 × 1.41 = 4512 – check the option directly.

Answer: (D) 3,200

Concept: Speed = (train + platform) ÷ time; opposite directions → add speeds.

1. Fast train: (300 + 600) ÷ 40 = 22.5 m/s.
2. Slow train: (450 + 600) ÷ 60 = 17.5 m/s.
3. Relative speed = 40 m/s; distance = 300 + 450 = 750 m.
4. Time = 750 ÷ 40 = 18.75 s.

Short trick: Total lengths ÷ sum of speeds: 750 ÷ 40 = 18.75.

Answer: (A) 18.75 seconds

Concept: Mode = most frequent value.

1. 89 appears 3 times (1st, 10th and 18th values).
2. 76, 81, 64, 65 and 87 appear twice each; the rest once.
3. Mode = 89.

Short trick: Check the options only: count 76, 64, 81, 89 – 89 is the only one with three.

Answer: (D) 89

Concept: For 2 years, CI − SI = interest on one year's SI: $P{\left(\frac{r}{100}\right)}^2$.

1. SI for 1 year = 66 ÷ 2 = ₹33 = $\frac{Pr}{100}$.
2. CI − SI = 1 = $33\times \frac{r}{100}$ ⇒ $r=\frac{100}{33}\mathrm{\%}$.
3. $P=\frac{33\times 100}{r}=33\times 33=1089$.

Short trick: $P=\frac{(\text{SI for 1 yr}{)}^2}{\text{CI}-\text{SI}}=\frac{{33}^2}{1}=1089$.

Answer: (A) 1089

Concept: Total profit from the 5% value, then divide in the ratio capital × time.

1. Total profit = 7036 × 20 = ₹1,40,720.
2. Rajesh : Naresh = 66,000 × 2 : 29,000 × 12 = 1,32,000 : 3,48,000 = 11 : 29.
3. Naresh = $\frac{29}{40}\times 140720=29\times 3518=102022$.

Short trick: 5% = 7036 → 1 share of 40 = 140720/40 = 3518; Naresh = 29 × 3518.

Answer: (B) 1,02,022

Concept: Arc length $l=\frac{\theta }{{360}^{\circ }}\times 2\pi r$.

1. $l=\frac{60}{360}\times 2\times \frac{22}{7}\times 6$.
2. $=\frac{1}{6}\times \frac{264}{7}=\frac{44}{7}$ units.

Short trick: 60° sector with r = 6: $l=\frac{\pi r}{3}=2\pi =\frac{44}{7}$.

Answer: (B) $\frac{44}{7}$

Concept: Work ∝ machines × hours: $\frac{M_1{H}_1}{W_1}=\frac{M_2{H}_2}{W_2}$.

1. $\frac{5\times 6}{9000}=\frac{M\times 8}{28800}$.
2. $M=\frac{5\times 6\times 28800}{9000\times 8}=12$.

Short trick: One printer prints 9000 ÷ 30 = 300 pages/hour; need 28800 ÷ 8 = 3600 pages/hour → 3600 ÷ 300 = 12.

Answer: (B) 12

Concept: When a transversal cuts two parallel lines, corresponding angles are equal.

1. The angle with the first line is ${65}^{\circ }$.
2. The corresponding angle (same position) on the other line is also ${65}^{\circ }$.
3. (Co-interior angles would be ${180}^{\circ }-{65}^{\circ }={115}^{\circ }$ – a trap option.)

Short trick: Corresponding = 'F' shape = equal; co-interior = 'C/U' shape = supplementary.

Answer: (A) ${65}^{\circ }$

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

1. $P=\frac{460\times 100}{10\times 4}$.
2. $=\frac{46000}{40}=1150$.

Short trick: 4 years at 10% = 40% of P = 460 → P = 460 × 2.5 = 1150.

Answer: (B) 1150

Concept: Work backwards from Minu's price.

1. Biru's total cost = 1053 ÷ 1.5 = 702.
2. Price Biru paid = 702 − 198 = 504.
3. Arvind sold at 30% loss: 0.7x = 504 ⇒ x = 720.

Short trick: Option check: 720 × 0.7 = 504; (504 + 198) × 1.5 = 1053 ✓.

Answer: (D) 720

Concept: SP = MP × (1 − d%) and SP = CP × (1 + profit%).

1. Let CP = 100 → MP = 140, SP = 110.
2. Discount = 140 − 110 = 30.
3. $d=\frac{30}{140}\times 100=\frac{150}{7}=21\frac{3}{7}\mathrm{\%}$

Short trick: $d\mathrm{\%}=\frac{\text{Markup}-\text{Profit}}{100+\text{Markup}}\times 100=\frac{40-10}{140}\times 100$

Answer: (C) $21\frac{3}{7}\mathrm{\%}$

Concept: Required SP = CP × (1 + gain%); discount is taken on MP.

1. Let CP = 100 → MP = 120.
2. Required SP = 102.
3. Discount = 120 − 102 = 18 → $\frac{18}{120}\times 100=15\mathrm{\%}$

Short trick: $\frac{20-2}{120}\times 100=15\mathrm{\%}$

Answer: (B) 15%

Concept: Interest of the 2nd year = interest of the 1st year + interest on that interest = $P\cdot r(1+r)$.

1. 1st-year interest $=\frac{3072}{1.2}=2560$
2. $P=\frac{2560}{0.20}=12800$

Short trick: $P=\frac{3072}{0.2\times 1.2}=\frac{3072}{0.24}=12800$

Answer: (B) ₹12800

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

1. $480=\frac{P\times 10\times 2}{100}=\frac{P}{5}$
2. $P=480\times 5=2400$

Short trick: Total rate = 10% × 2 = 20% → 20% of P = 480 → P = 480 × 5 = 2400.

Answer: (D) 2400

Concept: Overall profit % = weighted average of the individual profit % (weights = share of goods).

1. Shares: 50%, 32% of remaining 50% = 16%, rest = 34%.
2. Overall = 0.50 × 49 + 0.16 × 45 − 0.34 × 15
3. = 24.5 + 7.2 − 5.1 = 26.6%

Short trick: Take 100 units of cost 1 each: profit = 24.5 + 7.2 − 5.1 = 26.6 on 100 → 26.6%.

Answer: (B) 26.6%

Concept: Make equal decimal places, find LCM of the whole numbers, then put back the decimal.

1. 1.30, 7.60, 0.13 → 130, 760, 13 (÷100 later).
2. $130=2\times 5\times 13$, $760=2^3\times 5\times 19$, $13=13$
3. LCM $=2^3\times 5\times 13\times 19=9880$ → 98.8

Short trick: LCM must be divisible by 7.6 and 1.3: 98.8 ÷ 7.6 = 13 and 98.8 ÷ 1.3 = 76 – only 98.8 works.

Answer: (B) 98.8

Concept: Mode = the value that occurs most often.

1. 44 appears 3 times (positions 1, 16, 18).
2. 40, 42, 46, 51, 55 appear twice each; others once.
3. Mode = 44

Short trick: Scan only the options: 44 → 3 times, 51, 55, 40 → 2 times each.

Answer: (A) 44

Concept: Form the equation and reverse the operations.

1. $\frac{n}{3}+25=87\Rightarrow \frac{n}{3}=62$
2. $n=186$
3. Digit sum = 1 + 8 + 6 = 15

Short trick: Work backwards: (87 − 25) × 3 = 186.

Answer: (B) 15

Concept: Volume of water stays the same: $\frac{1}{3}\pi R^{2}H=\pi r^{2}h$.

1. $r=\frac{R}{3}$
2. $\frac{1}{3}\pi R^2(19)=\pi \frac{R^2}{9}h$
3. $h=\frac{19\times 9}{3}=57$ cm

Short trick: $h=\frac{H}{3}\times {\left(\frac{R}{r}\right)}^2=\frac{19}{3}\times 9=57$

Answer: (C) 57 cm

Concept: Area = ½ × base × height; with the same base, area ∝ height.

1. First triangle: $98=\frac{1}{2}\times 14\times h_1\Rightarrow h_1=14$ cm
2. Second area = 196 → $h_2=\frac{2\times 196}{14}=28$ cm

Short trick: Same base, area doubled → height doubled: 14 × 2 = 28 cm.

Answer: (B) 28 cm