RRB ALP CBT 1 2025 PYQs

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) $31250\pi$

Concept: Replace the letters by signs, then apply BODMAS.

1. 79 − 12 × 4 + 100 ÷ 5
2. = 79 − 48 + 20
3. = 51

Short trick: Do × and ÷ first (48 and 20), then 79 − 48 + 20 = 51.

Answer: (A) 51

Concept: Check the position gaps inside each cluster and between the pairs.

1. Pair	Pattern
   PM - OL	P−3=M; P−1=O, O−3=L
   MJ - LI	M−3=J; L−3=I
   VS - UR	V−3=S; U−3=R
   TQ - KO	T−3=Q but K+4=O, and T→K is −9

Short trick: In the three alike pairs the second cluster is the first cluster shifted back by one letter (PM→OL). TQ→KO breaks it.

Answer: (B) TQ - KO

Concept: Draw the minimum (least overlapping) Venn diagram and test each conclusion.

1. Some doctors are eagles → Doctors and Eagles overlap.
2. No snake is a doctor → Snakes lie outside Doctors.
3. (I) The eagles that are doctors can never be snakes → some eagles are not snakes. Follows.
4. (II) Only some eagles are known to be doctors → "All eagles are doctors" does not follow.

Short trick: "Some A are B" + "No C is A" ⇒ "Some B are not C" always follows (the A-part of B is safe from C).

Answer: (D) Only conclusion (I) follows.

Concept: Check whether any member can belong to two classes at once.

1. Carrot is a vegetable (root); apple and lime are different fruits.
2. No carrot is an apple or a lime, and no apple is a lime.
3. So the three classes are completely separate → three disjoint circles.

Short trick: Three different items of the same level (no item is both) → three separate circles.

Answer: (B) Three separate circles (option B)

Concept: Take P = (0, 0), north = +y, east = +x and trace each move.

1. 8 m north → (0, 8); right (east) 5 m → (5, 8)
2. Right (south) 4 m → (5, 4); right (west) 10 m → (−5, 4)
3. Left (south) 4 m → Q = (−5, 0)
4. Q is 5 m west of P, so she must walk East.

Short trick: Net N–S: 8 − 4 − 4 = 0; net E–W: 5 − 10 = 5 m west. Q is due west of P, so go East.

Answer: (C) East

Concept: Look for the pattern consonant–CONSONANT–vowel. Vowels in the series: E and A only.

1. Check the letter just before each vowel: before E is N (first letter, nothing precedes it); before A is J.
2. J is preceded by G (consonant) and followed by A (vowel) ✓
3. Only one such consonant: J.

Short trick: Start from the vowels (few) and look two places back — much faster than scanning every letter.

Answer: (A) One

Concept: Find the differences between consecutive terms.

1. 108 −5 → 103 −6 → 97 −7 → 90 −8 → 82 −9 → 73
2. Next difference = −10
3. 73 − 10 = 63

Short trick: Differences are 5, 6, 7, 8, 9 → next 10.

Answer: (C) 63

Concept: Find the shift for each letter position.

1. 	1st	2nd	3rd
   KFM → GCR	K−4=G	F−3=C	M+5=R
   RMS → NJX	R−4=N	M−3=J	S+5=X
   MSU → IPZ	M−4=I	S−3=P	U+5=Z ✓

Short trick: The first letter (−4) fits every option, so test the second letter (−3) at once: S→P ✓, while R→N, O→J, S→N fail.

Answer: (A) MSU : IPZ

Concept: Build the family tree.

1. B is the son of C, and A is the brother of B → A is also a child of C.
2. A is a brother → male.
3. So A is the son of C. (M, Q and D are extra information.)

Short trick: "Brother of my son" = my son. Ignore the spouse/daughter details.

Answer: (C) Son

Concept: Swap + ↔ − and × ↔ ÷, then use BODMAS.

1. 6 × 45 ÷ 15 + 8 − 13 becomes 6 ÷ 45 × 15 − 8 + 13
2. $6÷45\times 15=\frac{6\times 15}{45}=2$
3. 2 − 8 + 13 = 7

Short trick: $\frac{6\times 15}{45}=2$ directly, then 2 + 5 = 7.

Answer: (A) 7