RRB NTPC Graduate CBT 1 2024 PYQs

Concept: Form two linear equations and solve.

1. $6A+4B=156$ and $2B-9A=30\Rightarrow 4B=18A+60$
2. $6A+18A+60=156\Rightarrow 24A=96\Rightarrow A=4$
3. $2B=30+36=66\Rightarrow B=33$
4. After 9 years: $(4+9)+(33+9)=55$

Trick: Sum after n years = present sum + 2n = $37+18$.

Answer: (D) 55

Concept: Going back n years: $P_{-n}=\frac{P}{(1+r{)}^n}$, with $1.25=\frac{5}{4}$.

1. 2 years ago $=260000\times {\left(\frac{4}{5}\right)}^2=166400$
2. 3 years ago $=166400\times \frac{4}{5}=133120$
3. Difference $=166400-133120=33280$

Trick: Difference = 20% of the 2-years-ago value: $\frac{166400}{5}=33280$.

Answer: (A) 33,280

Concept: Saving % = 100% − spending %.

1. Saving $=100\%-52\%=48\%$ = ₹7,740
2. 1% = $\frac{7740}{48}=161.25$
3. Expenses $=52\times 161.25=$ ₹8,385

Trick: Expenses $=7740\times \frac{52}{48}=7740\times \frac{13}{12}=8385$.

Answer: (B) 8,385

Concept: Leak rate = filling rate − net rate.

1. Pump rate $=\frac{1}{8}$; net rate $=\frac{3}{28}$ (since $9\frac{1}{3}=\frac{28}{3}$)
2. Leak $=\frac{1}{8}-\frac{3}{28}=\frac{7-6}{56}=\frac{1}{56}$
3. Leak empties the tank in 56 hours.

Trick: Leak time $=\frac{ab}{b-a}=\frac{8\times \frac{28}{3}}{\frac{28}{3}-8}=56$.

Answer: (B) 56 hours

Concept: $\text{CSA}=2\pi rh,\text{TSA}=2\pi r(r+h),V=\pi r^{2}h$

1. $2\pi rh=\frac{1}{2}\times 2\pi r(r+h)\Rightarrow 2h=r+h\Rightarrow r=h$
2. $r=h=10\text{cm}$
3. $V=\pi \times {10}^2\times 10=1000\pi {\text{cm}}^3$

Trick: CSA = half TSA ⇔ CSA = area of the two ends ⇔ $r=h$.

Answer: (B) $1000\pi$

Concept: Price after discounts = MP × product of $(1-d)$ factors.

1. $0.82\times 0.76\times 0.82$
2. $0.82\times 0.82=0.6724$
3. $0.6724\times 0.76=0.511024\approx 51.10\%$

Trick: Two equal 18% discounts: ${0.82}^2=0.6724$ first, then ×0.76.

Answer: (A) 51.10%

Concept: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

1. $a=3,b=-7,c=1$
2. $D=49-12=37$
3. $x=\frac{7\pm \sqrt{37}}{6}$

Trick: Sum of roots $=\frac{7}{3}$ must be positive — check options with it.

Answer: (B) $\frac{7+\sqrt{37}}{6}$ & $\frac{7-\sqrt{37}}{6}$

Concept: Profit% = $\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100$ on the goods actually given.

1. He charges for 1134 g: $\text{SP}=1.134\times 17=19.278$
2. He gives 567 g: $\text{CP}=0.567\times 20=11.34$
3. Profit $=7.938$; $\%=\frac{7.938}{11.34}\times 100=70\%$

Trick: $\frac{\text{SP}}{\text{CP}}=\frac{17}{20}\times \frac{1134}{567}=\frac{17}{10}=1.7$ → 70% profit.

Answer: (C) Profit of 70%

Concept: B's rate = combined rate − A's rate.

1. $\frac{1}{14}-\frac{1}{56}=\frac{4-1}{56}=\frac{3}{56}$
2. B alone: $\frac{56}{3}$ days
3. $\frac{3}{4}$ work: $\frac{3}{4}\times \frac{56}{3}=14$ days

Trick: Total work 56 units: A = 1, B = 3 per day; $\frac{3}{4}$ of 56 = 42 → $42÷3=14$.

Answer: (A) 14

Concept: $\text{Area of sector}=\frac{1}{2}\times l\times r$

1. $l=5,r=16.2$
2. $\text{Area}=\frac{1}{2}\times 5\times 16.2=40.5$ sq units

Trick: No angle needed when arc length is given.

Answer: (B) 40.5 units²

Concept: Track the position as coordinates, taking Y as origin, East as $+x$ and North as $+y$.

1. East 47: $(47,0)$; right turn → South 23: $(47,-23)$.
2. Right → West 26: $(21,-23)$; right → North 52: $(21,29)$.
3. Left → West 21: $(0,29)$; left → South 11: $Z=(0,18)$.
4. Z is 18 km directly north of Y, so he must drive 18 km towards the south.

Trick: Net E–W: $47-26-21=0$; net N–S: $-23+52-11=18$ north. Return trip is the opposite direction.

Answer: (B) 18 km towards the south

Concept: Facing the centre, “left” means moving clockwise and “right” anticlockwise.

1. Fix F; B is third to the left of F.
2. Only F sits between A and C, so A and C are on either side of F; with C second to the left of D, only the order C, F, A (clockwise) with D two places right of C works.
3. G is not next to B, so E sits beside B and A: order clockwise A, E, B, D, G, C, F.
4. From the left of D (clockwise): D → G, C, F → A, i.e. 3 people between.

Trick: Place the person named most often (F) first, then fix the “only one between” clue.

Answer: (D) Three

Concept: Find the letter shift from the right pair and apply it to the left pair.

1. Option B: F+5 = K, N+5 = S, W+5 = B (after Z, back to A), so FNW → KSB.
2. Apply +5 to NVE: N+5 = S, V+5 = A, E+5 = J → SAJ.
3. Both blanks are satisfied only by # = FNW, % = SAJ.

Trick: Check each option’s shift on the first pair; the matching one must give the same shift on the second pair.

Answer: (B) # = FNW, % = SAJ

Concept: Check every symbol: the element just before and just after it must both be numbers.

1. 7 € 2 ✓, 3 © 8 ✓, 8 © 4 ✓, 4 € 9 ✓, 3 € 5 ✓, 7 $ 1 ✓.
2. #, % and * fail (they are next to other symbols).
3. Total = 6.

Trick: Skip blocks of consecutive symbols — none of them can qualify.

Answer: (C) 6

Concept: Decode each symbol step by step and draw the family tree.

1. P + Q: P is sister of Q (P female).
2. Q – R: Q is father of R; R ÷ S: R is son of S, so S is R’s mother and Q’s wife.
3. S × T: S is daughter of T.
4. So Q is T’s daughter’s husband, and P is his sister: P is T’s daughter’s husband’s sister.

Trick: Write relations from T’s side backward: T → daughter S → her husband Q → his sister P.

Answer: (A) Daughter’s husband’s sister

Concept: Compare positions: each letter of the first cluster vs the matching letter of the second cluster.

1. NP – KM: N−3 = K, P−3 = M.
2. KM – HJ: K−3 = H, M−3 = J; HJ – EG: H−3 = E, J−3 = G.
3. MP – LK: M−1 = L, P−5 = K — different rule.

Trick: Three pairs show a uniform −3 shift; the one breaking it is odd.

Answer: (A) MP - LK

Concept: First identify the highest and lowest numbers, then pick the required digits.

1. Highest = 930 → first digit 9.
2. Lowest = 335 → third digit 5.
3. $9+5=14$.

Trick: Compare first digits only: 9 is highest, 3 is lowest.

Answer: (D) 14

Concept: Find the shift in the first pair and repeat it in the second pair.

1. Option B: T−3 = Q, V−3 = S, R−3 = O, so TVR → QSO.
2. XZV with −3: X→U, Z→W, V→S = UWS.

Trick: Letters QSO are spaced +2, −4; the answer cluster must keep the same spacing (UWS: +2, −4).

Answer: (B) # = TVR, % = UWS

Concept: Find the position-wise change from the first cluster to the second.

1. HMP → KON: H+3, M+2, P−2.
2. USQ → XUO: U+3, S+2, Q−2.
3. DLV → GNT: D+3 = G, L+2 = N, V−2 = T ✓.

Trick: Test only the first letter (+3) to shortlist: KWZ (−4) and DWP (+6), BIO (+4) fail at once.

Answer: (B) DLV : GNT

Concept: Look at the differences between consecutive terms.

1. Differences: $428-405=23$, $405-372=33$ — increasing by 10.
2. Next difference 43: $372-43=329$.
3. Check: $329-53=276$, $276-63=213$ ✓.

Trick: Differences 23, 33, 43, 53, 63 — an arithmetic pattern of +10.

Answer: (A) 329