RRB NTPC Graduate Level (19th March 2026 Shift 2) — RRB NTPC 2025

• Given: A sum becomes $5$ times itself in $T = 18$ years on Simple Interest. Rate $R = ?$

• Basic Method (Solution):
Step 1: Let the principal be $P$. If it becomes $5$ times, the Amount $A = 5P$.
Step 2: Simple Interest (SI) = Amount - Principal = $5P - P = 4P$.
Step 3: Formula for SI is $SI = \frac{P \times R \times T}{100}$.
Step 4: Substitute the values: $4P = \frac{P \times R \times 18}{100}$.
Step 5: Cancel $P$ from both sides: $4 = \frac{18R}{100} \implies 18R = 400 \implies R = \frac{400}{18} = \frac{200}{9}$.
Step 6: $R = 22.222... \%$, which rounds off to $22.22\%$.

• Shortcut Method: For a sum to become 'n' times in 'T' years at SI, Rate $R = \frac{(n-1) \times 100}{T}$. Here $n=5, T=18$. $R = \frac{(5-1) \times 100}{18} = \frac{400}{18} = \frac{200}{9} = 22.22\%$.

• Final Answer: 22.22

• Given: Initial investment ratio $X:Y:Z = 6:3:5$. Z's investment = 12000 (redundant for ratio). X withdraws half after 6 months. Total annual profit = 69000. Find difference between X and Y profit.

• Basic Method (Solution):
Step 1: Profit is distributed in the ratio of (Investment $\times$ Time).
Step 2: Let the initial investments be $6u, 3u, 5u$.
Step 3: X's equivalent capital $= (6u \times 6 \text{ months}) + (3u \times 6 \text{ months}) = 36u + 18u = 54u$.
Step 4: Y's equivalent capital $= 3u \times 12 \text{ months} = 36u$.
Step 5: Z's equivalent capital $= 5u \times 12 \text{ months} = 60u$.
Step 6: Profit ratio $X : Y : Z = 54u : 36u : 60u = 54 : 36 : 60$. Divide by 6: $9 : 6 : 10$.
Step 7: Total parts $= 9 + 6 + 10 = 25$ parts.
Step 8: Value of 1 part $= \frac{69000}{25} = 2760$.
Step 9: Difference between X and Y's profit $= 9 \text{ parts} - 6 \text{ parts} = 3 \text{ parts}$.
Step 10: Difference $= 3 \times 2760 = 8280$.

• Shortcut Method: Ignore the absolute value of Z's investment (12000) as profit sharing only needs the ratio.
Ratio of profits $X : Y : Z = [6 \times 6 + 3 \times 6] : [3 \times 12] : [5 \times 12] = 54 : 36 : 60 = 9 : 6 : 10$.
Total $= 25$ units $= 69000$.
Diff (X-Y) $= 3$ units.
Value $= \frac{3}{25} \times 69000 = 3 \times 2760 = 8280$.

• Final Answer: ₹8280

• Key Fact: J.J. Thomson determined the specific charge, or the charge-to-mass ratio ($e/m$), of an electron in 1897 using a cathode ray tube.

• Supporting Detail: By applying both magnetic and electric fields perpendicular to the path of the cathode rays, he was able to calculate this ratio, which was a fundamental step in the discovery of the electron itself.

• Related Concept: Later, Robert Millikan determined the exact charge of a single electron ($e$) through his famous oil-drop experiment, allowing the exact mass ($m$) to finally be calculated.

• Why others wrong: Einstein is known for the photoelectric effect and relativity; Bohr proposed the quantized planetary model of the atom; Newton formulated the laws of classical mechanics and universal gravitation.

• Exam Trick: Remember that Thomson discovered the electron, and finding the e/m ratio was the very experiment that proved electrons were subatomic particles much smaller than atoms.

• Additional Info: The accepted value for the $e/m$ ratio of an electron is approximately $1.75882 \times 10^{11}$ C/kg.

• Given conditions:
+ means Son
- means Brother
$\times$ means Wife
$\div$ means Father
Equation: $W - O \times R + K \div G$. Wait, the image for question 4 shows a slightly different fourth symbol. Let me look closely. The fourth statement is "A $\div$ B means A is the father of B". But in the expression it says "$R + K \div G$"? No, looking at the image it is a plus sign: $A + B$ means father?
Let's re-read the OCR text and the image carefully.
OCR: A + B means 'A is the son of B'
A - B means 'A is the brother of B'
A x B means 'A is the wife of B'
A $\div$ B means 'A is the father of B'
Expression: $W - O \times R + K \div G$. (Actually, the image text for the fourth condition looks like A $\div$ B but it has a horizontal line and two dots, yes it's $\div$. Let's assume the OCR is correct).

• Deduction process:
Let's break down the expression $W - O \times R + K \div G$ from left to right:
1. $W - O$: W is the brother of O. So, W(+), O(gender unknown yet).
2. $O \times R$: O is the wife of R. So, O(-), and they are married to R(+).
3. $R + K$: R is the son of K. So, K is the parent of R.
4. $K \div G$: K is the father of G. So, K(+), and G is the sibling of R.
Now, relate W to G:
G's brother is R.
R's wife is O.
O's brother is W.
So, W is the brother of O, who is the wife of R, who is the brother of G.
From G's perspective: R is G's brother. O is G's brother's wife. W is G's brother's wife's brother.
Wait, let's re-read the options.
A. Brother's wife's brother
B. Brother's wife's father
C. Wife's father
D. Wife's brother
Our derivation "Brother's wife's brother" matches Option A perfectly.

• Exam Trick: Break the chain into small pieces. G's brother (R) $\rightarrow$ his wife (O) $\rightarrow$ her brother (W). Thus, Brother's wife's brother.

• Final Answer: Brother's wife's brother

• Given conditions: $10 \rightarrow 120$, $12 \rightarrow 168$. Find $18 \rightarrow ?$

• Deduction process:
Let's test common patterns (squares, multiples).
Look at 10 and 120: $10^2 = 100$. $120$ is $100 + 20$. So, $N^2 + 2N$.
Look at 12 and 168: $12^2 = 144$. $144 + 2(12) = 144 + 24 = 168$. The pattern holds perfectly.
The logic is $x \rightarrow x^2 + 2x$, which is also $x(x+2)$.
Let's check $10(10+2) = 10 imes 12 = 120$. Correct.
Let's check $12(12+2) = 12 imes 14 = 168$. Correct.
Now apply it to 18:
$18 \rightarrow 18(18+2) = 18 \times 20 = 360$.
Or using squares: $18^2 + 2(18) = 324 + 36 = 360$.

• Exam Trick: When you see a number jumping slightly above its square (e.g., 10 to 120, 12 to 168), immediately check the difference between the number and its square. Here, differences are 20 and 24, which are exactly double the original numbers.

• Final Answer: 360

• Given conditions: 6 floors (1 to 6). X on even (not 4). 2 people between X and T. S on odd (not 1). 2 people between S and Y. Z immediately below S. Find people between U and Z.

• Deduction process:
1. X is on an even floor (2, 4, or 6). Since X is not on 4, X is on 2 or 6.
2. S is on an odd floor (1, 3, or 5). Since S is not on 1, S is on 3 or 5.
3. Z lives immediately below S. If S is on 5, Z is on 4. If S is on 3, Z is on 2.
4. Let's test S = 5. Then Z = 4.
Two people between S(5) and Y $\implies$ Y must be on floor 2.
Now where is X? X can be on 2 or 6. But floor 2 is occupied by Y. So X MUST be on floor 6.
Two people between X(6) and T $\implies$ T must be on floor 3.
The only remaining person is U, who must take the last empty floor, which is floor 1.
Let's check all conditions for this arrangement (6=X, 5=S, 4=Z, 3=T, 2=Y, 1=U):
X on even not 4 (X is on 6 - OK).
2 people between X(6) and T(3) (S and Z are between them - OK).
S on odd not 1 (S is on 5 - OK).
2 people between S(5) and Y(2) (Z and T are between them - OK).
Z immediately below S (Z is 4, S is 5 - OK).
This arrangement works perfectly.
5. Question: How many people live between U(1) and Z(4)?
Between floor 1 and floor 4 are floors 2 and 3. That is 2 people (Y and T).

• Exam Trick: "Immediately below" combined with an "odd/even restriction" is the best place to start creating hypothetical cases. S=5 quickly forces Y, X, and T into place.

• Final Answer: Two

• Given conditions: WINS = 8246. NORM = 3851. Code for N = ?

• Deduction process:
Compare the two words: WINS and NORM.
Common letter between WINS and NORM is 'N'.
Look at their codes: 8246 and 3851.
The only common digit between 8246 and 3851 is '8'.
Therefore, the common letter 'N' must correspond to the common digit '8'.

• Exam Trick: Find the intersection of letters and the intersection of numbers. This is a direct substitution cipher.

• Final Answer: 8

• Given conditions: Original number: 8371456. Rule: Odd + 1, Even - 2. Find sum of 2nd from left and 2nd from right in the new number.

• Deduction process:
Step 1: Identify the target digits in the original number first to save time.
Original number: 8 3 7 1 4 5 6
2nd from left = 3 (Odd)
2nd from right = 5 (Odd)
Step 2: Apply the rules to only these two digits.
New 2nd from left: $3 + 1 = 4$.
New 2nd from right: $5 + 1 = 6$.
Step 3: Find their sum.
Sum $= 4 + 6 = 10$.

• Exam Trick: Do not rewrite the entire 7-digit number. Only calculate the new values for the specific positions requested in the final question.

• Final Answer: 10

• Key Fact: India officially joined the Shanghai Cooperation Organization (SCO) as a full member in 2017 at the historic Astana summit.

• Supporting Detail: Pakistan also joined the SCO as a full member simultaneously at the same summit, expanding the group's footprint into South Asia.

• Related Concept: Prior to 2017, India had observer status in the SCO since 2005.

• Why others wrong: 2008 and 2012 are years when India was still an observer. 2021 is when Iran's process to become a full member was approved.

• Exam Trick: Remember that India and Pakistan joined this major Eurasian political and security group together in 2017.

• Additional Info: The SCO was founded in 2001 in Shanghai by the leaders of China, Kazakhstan, Kyrgyzstan, Russia, Tajikistan, and Uzbekistan.

• Given conditions: Series: YQM 2, SKG 6, MEA 12, GYU 20, ?

• Deduction process:
Analyze the number pattern first:
$2 \rightarrow 6 \rightarrow 12 \rightarrow 20 \rightarrow ?$
Differences: $6-2 = 4$; $12-6 = 6$; $20-12 = 8$.
The differences are increasing by 2 ($4, 6, 8$). The next difference is 10.
So the next number is $20 + 10 = 30$. This eliminates Option A.
Analyze the first letter pattern:
Y(25) $\rightarrow$ S(19) $\rightarrow$ M(13) $\rightarrow$ G(7) $\rightarrow$ ?
Pattern: $-6, -6, -6$.
$7 - 6 = 1$. The 1st letter is A. This completely locks Option B without further checks.
For thoroughness, let's check the other letters:
Second letter: Q(17) $\rightarrow$ K(11) $\rightarrow$ E(5) $\rightarrow$ Y(25, which is $5-6$ due to wrap-around) $\rightarrow$ ? ($25-6 = 19$, which is S).
Third letter: M(13) $\rightarrow$ G(7) $\rightarrow$ A(1) $\rightarrow$ U(21, which is $27-6$) $\rightarrow$ ? ($21-6 = 15$, which is O).
The cluster is ASO 30.

• Exam Trick: Always solve the first letter and the number first. A unique combination (like starting with 'A' and ending with '30') saves time checking the middle letters.

• Final Answer: ASO 30