RRB NTPC Graduate CBT 1 2024 PYQs

Concept: One-day work of B = (A + B)'s one-day work − A's one-day work.

1. $\frac{1}{B}=\frac{1}{6}-\frac{1}{7}=\frac{7-6}{42}=\frac{1}{42}$.
2. So B alone takes 42 days.

Trick: B's time $=\frac{6\times 7}{7-6}=42$ days.

Answer: (B) 42

Concept: Mean proportional of $a$ and $b$ $=\sqrt{ab}$.

1. $\sqrt{0.09\times 16}=\sqrt{1.44}$.
2. $\sqrt{1.44}=1.2$.

Trick: $\sqrt{0.09}\times \sqrt{16}=0.3\times 4=1.2$.

Answer: (C) 1.2

Concept: If every number is increased by the same amount, the average increases by that amount.

1. Old average = 18.
2. Each number + 5 → new average $=18+5=23$.
3. Check: sum $=6\times 18=108$, new sum $=108+30=138$, $\frac{138}{6}=23$.

Trick: Add / subtract / multiply every item by $k$ → do the same to the average.

Answer: (C) 23

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

1. Upstream speed $=\frac{59.4}{18/60}=198\text{km/h}$.
2. $b:s=3:2$ → upstream $=3-2=1$ part $=198$, downstream $=3+2=5$ parts $=990\text{km/h}$.
3. Time $=\frac{29.3}{198}+\frac{51.5}{990}=\frac{146.5+51.5}{990}=\frac{198}{990}=0.2\text{h}$.

Trick: Write both times over 990: upstream distance × 5 + downstream distance $=146.5+51.5=198$.

Answer: (D) 0.2

Concept: Supplementary angles add up to ${180}^{\circ }$.

1. Let smaller angle $=x$, larger $=x+{60}^{\circ }$.
2. $x+x+{60}^{\circ }={180}^{\circ }\Rightarrow 2x={120}^{\circ }$.
3. $x={60}^{\circ }$ (larger $={120}^{\circ }$).

Trick: Smaller $=\frac{{180}^{\circ }-{60}^{\circ }}{2}={60}^{\circ }$.

Answer: (C) ${60}^{\circ }$

Concept: For $a{x}^3+b{x}^2+cx+d=0$, sum of roots $=-\frac{b}{a}$.

1. Here $a=2$, $b=7$.
2. Sum of roots $=-\frac{7}{2}$.

Trick: Sum $=-\frac{b}{a}$, product $=-\frac{d}{a}$ for a cubic; options $\frac{9}{2}$ or $-\frac{2}{7}$ come from using wrong coefficients.

Answer: (C) $\frac{-7}{2}$

Concept: $\text{Mode}=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$.

1. Mode 125 lies at the boundary; take modal class 120-125: $l=120$, $f_1=39$, $f_0=31$, $f_2=x$, $h=5$.
2. $125=120+\frac{39-31}{78-31-x}\times 5\Rightarrow \frac{8}{47-x}\times 5=5$.
3. $47-x=8\Rightarrow x=39$.

Trick: Mode = upper limit $l+h$ needs $f_1-f_0=2f_1-f_0-f_2$, i.e. $f_2=f_1$, so $x=39$.

Answer: (D) 39

Concept: Solve innermost brackets first; ÷ and × are done left to right.

1. $18-\frac{14}{2}=18-7=11$.
2. $7÷7\times 11=1\times 11=11$.
3. $(17\times 3)\times 11=51\times 11=561$.

Trick: $51\times 11$: write 5, (5+1), 1 → 561.

Answer: (C) 561

Concept: Mahesh's age = (sum of ages) − (Ramesh's age); subtract like terms.

1. $(2x^2-3x^{2}y+y^2+3x{y}^2)-(x^2+3x^{2}y+y^2+3x{y}^2)$.
2. $x^2$ terms: $2x^2-x^2=x^2$; $x^{2}y$ terms: $-3x^{2}y-3x^{2}y=-6x^{2}y$.
3. $y^2$ and $3x{y}^2$ cancel. Result: $(x^2-6x^{2}y)$ years.

Trick: Only the unlike-sign terms survive – look for $x^{2}y$, which rules out options with $xy$.

Answer: (A) $(x^2-6x^{2}y)$ years

Concept: Savings % $=100\%-\text{Expenditure}\%$.

1. Savings $=100\%-55\%=45\%$ of income = ₹6,408.
2. Income $=\frac{6408}{0.45}=$ ₹14,240.
3. Expenses $=0.55\times 14240=$ ₹7,832.

Trick: Expenses $=6408\times \frac{55}{45}=6408\times \frac{11}{9}=712\times 11=$ ₹7,832.

Answer: (A) 7,832

Concept: Apply the rule digit by digit: odd digit +1, even digit −2.

1. 7125843 → 7→8, 1→2, 2→0, 5→6, 8→6, 4→2, 3→4
2. New number: 8206624
3. Highest digit 8, lowest digit 0; sum $=8+0=8$

Trick: Only the extreme digits matter – check which digit can become the largest (7 or 8 → 8) and the smallest (2 → 0).

Answer: (D) 8

Concept: Total $=\text{rank from top}+\text{rank from bottom}-1$ (the person is counted twice).

1. Total $=34+25-1$
2. $=58$

Trick: Add both ranks and subtract 1.

Answer: (C) 58

Concept: Look for the pattern: number – symbol – symbol.

1. Symbols in the series: £, &, ©, $, ©, %, #, ©.
2. £: preceded by 3, followed by & ✓
3. #: preceded by 3, followed by © ✓
4. Others are followed by a number (© 2, $ 9, © 9, % 9) or preceded by a symbol (&, last ©).

Trick: Scan only the symbols that are directly after a number, then check the next item.

Answer: (A) 2

Concept: Check the differences between consecutive terms.

1. Differences: $3,9,27,81$ – powers of 3.
2. Next difference $=243$
3. $125+243=368$

Trick: Also: each term $=\text{previous}\times 3-7$: $125\times 3-7=368$.

Answer: (D) 368

Concept: A letter common to two words takes the digit common to their two codes.

1. DISH → 4268, HUNT → 3527
2. Common letter: H; common digit: 2
3. So H = 2

Trick: Match the common letter with the common number – no order needed.

Answer: (A) 2

Concept: Find the rule from the right pair's pattern and test it on the left pair.

1. Option A: ZTP → WQM: Z−3=W, T−3=Q, P−3=M
2. Same rule: TNJ → T−3=Q, N−3=K, J−3=G → QKG
3. Both # = ZTP and % = QKG fit.

Trick: Each letter moves back 3 places in both pairs.

Answer: (A) # = ZTP, % = QKG

Concept: Use alphabet positions (A = 1 … Z = 26) and find the change for each part.

1. TN 14 → PK 29: T(20)−4 = P(16), N(14)−3 = K(11), $14+15=29$
2. JD 3 → FA 18: J−4 = F, D−3 = A, $3+15=18$ ✓
3. SG −5: S(19)−4 = O, G(7)−3 = D, $-5+15=10$ → OD 10

Trick: Fix the rule from two pairs; option D (OD 8) is a trap for $-5$ handled wrongly.

Answer: (C) OD 10

Concept: Decode each symbol and build the family tree.

1. P × Q: P is the wife of Q.
2. Q – R: Q is the brother of R.
3. R + S: R is the mother of S; S ÷ T: S is the father of T.
4. R is T's father's mother, and Q is R's brother.

Trick: Read the chain backwards from T: father → mother → brother.

Answer: (C) Father's mother's brother

Concept: Each letter position and the number follow their own steady pattern.

1. 1st letters: E, F, G, H → I (+1)
2. 2nd letters: J, K, L, M → N; 3rd: M, N, O, P → Q
3. Numbers: 13, 15, 17, 19 → 21 (+2)

Trick: All three letters move +1; number moves +2 → INQ 21.

Answer: (B) INQ 21

Concept: Compare each letter of the first cluster with the matching letter of the second (positions, cyclic after Z).

1. TL – BV: T+8 = B, L+10 = V
2. PH – XR: P+8 = X, H+10 = R
3. ZR – HB: Z+8 = H, R+10 = B
4. GY – OJ: G+8 = O, but Y+10 = I, not J ✗

Trick: Rule +8, +10 fails only in GY – OJ.

Answer: (C) GY – OJ