BPSC (Bihar) - MCQ Practice Questions

Understanding:

We need to find the length of the platform given the train's speed, the time to cross the platform, and the length of the train.

Formula:

When a train crosses a platform, the total distance covered equals the sum of the lengths of the train and the platform:

Step 1: Convert speed to m/s

Step 2: Calculate total distance covered

Step 3: Find length of platform

Answer:

The length of the platform is 300 metres.

Quick Tip:

Always convert km/h to m/s by multiplying by $\frac{5}{18}$ before using time in seconds.

Understanding:

We need to find the number of students who play neither sport.

Formula:

Step 1: Find students who play at least one sport

Step 2: Find students who play neither

Answer:

10 students play neither cricket nor football.

Understanding:

The principal doubles in 8 years under simple interest. We need to find the annual rate.

Formula:

Step 1: Substitute known values

Since $\text{SI}=P$:

Step 2: Solve for $R$

Answer:

The rate of interest per annum is 12.5%.

Quick Tip:

For simple interest, if a sum doubles in $T$ years, the rate $=\frac{100}{T}\%$.

Understanding:

We need to find the profit percentage when goods are marked up by 25% and then discounted by 10%.

Formula:

Step 1: Assume cost price $\text{CP}=100$

Step 2: Calculate selling price after discount

Step 3: Calculate profit percentage

Answer:

The shopkeeper earns a profit of 12.5%.

Quick Tip:

A quick formula: if mark-up is $a\%$ and discount is $b\%$, net profit $\%=a-b-\frac{ab}{100}$. Here: $25-10-\frac{25\times 10}{100}=15-2.5=12.5\%$.

Understanding:

We need to determine the seating arrangement of six people and find who sits at the other end (opposite to D).

Step 1: Use the given clues

Step 2: Build the arrangement

Since A B C are consecutive and E is between C and F:

Step 3: Identify the other end

With arrangement D A B C E F, D is at the left end and F is at the right end.

Answer:

F is sitting at the other end.

Quick Tip:

In linear arrangement puzzles, place the most constrained blocks first (consecutive triplets like ABC), then fit the remaining pieces around the end conditions.

Understanding:

We must decode the language by comparing phrases to identify which digit corresponds to 'you'.

Step 1: List the given information

Step 2: Identify the code for 'go'

Compare '15' (you go) and '59' (go come). The common word is 'go' and the common digit is $5$.

So $5=$ 'go'.

Step 3: Identify the code for 'you'

In '15' (you go), $5=$ 'go', so the remaining digit $1=$ 'you'.

Step 4: Verify using the third phrase

In '59' (go come), $5=$ 'go' and $9=$ 'come'. ✓

In '93' (they come), $9=$ 'come' and $3=$ 'they'. ✓

Answer:

The code for 'you' is 1.

Quick Tip:

In coding-decoding with number phrases, always look for the digit common to two phrases that share exactly one word — that common digit is the code for the shared word.

Understanding:

We need to find the next term in the series 3, 7, 13, 21, 31, ?

Step 1: Find differences between consecutive terms.

Step 2: Identify the pattern in differences.

The differences are 4, 6, 8, 10 — each increasing by 2. So the next difference is $10+2=12$.

Step 3: Find the next term.

Answer:

The next term in the series is 43.

Quick Tip:

Always check second-level differences when first differences are not constant — arithmetic progression of differences is a very common pattern in BPSC reasoning questions.

Understanding:

We need to find the relationship between the woman and the man she is pointing to.

Step 1: Decode the statement.

The woman says, "His mother is the only daughter of my mother."

Step 2: Identify "the only daughter of my mother."

"The only daughter of my mother" means the woman herself (since the only daughter of her mother is she).

Step 3: Conclude the relationship.

So, the man's mother = the woman herself.

Therefore, the woman is the man's mother.

Answer:

The woman is the Mother of the man.

Understanding:

We need to find the code for CANDLE using the same coding rule applied to FRIEND → HUMJTK.

Step 1: Find the shift pattern from FRIEND to HUMJTK.

Each letter is shifted by an increasing value starting at $+2$.

Step 2: Apply the same pattern to CANDLE.

(Using standard alphabet positions: $C=3,A=1,N=14,D=4,L=12,E=5$.)

Step 3: Combine the coded letters.

Answer:

The code for CANDLE is EDRIRG.

Quick Tip:

When the shift increases by 1 each position, write out the shifts (2, 3, 4, 5, 6, 7) and apply them to each letter in order — this prevents careless mistakes.

Understanding:

We need to find the final distance and direction from the starting point.

Step 1: Set up coordinates. Start at origin $(0,0)$.

Step 2: Find distance from starting point $(0,0)$ to $(-6,0)$.

Step 3: Determine direction.

The final position is at $(-6,0)$, which is directly West of the origin.

Answer:

The man is $6$ km West of his starting point.

Quick Tip:

For direction problems, use a coordinate grid. "Turn left" when facing North means turning West; "turn left" again from West means facing South.

Understanding:

We need to find the time to fill the tank when both pipes are open simultaneously.

Formula:

Step 1: Find the net filling rate per hour.

Step 2: Find total time to fill the tank.

Answer:

The tank will be completely filled in 36 hours.

Quick Tip:

When a filling pipe is slower than the emptying pipe, the tank never fills. Always check that the filling rate is greater than the emptying rate before solving.

Understanding:

We need to find Suresh's position from the right end in a row of 40 students.

Step 1: Find Suresh's position from the left.

Step 2: Find Suresh's position from the right.

Answer:

Suresh's position from the right end is 16th.

Quick Tip:

The standard formula — Position from right $=n-\text{position from left}+1$ — works for any linear arrangement. Memorise it to save time.

Understanding:

We need to find the angle between the hour and minute hands at $3:25$.

Formula:

where $H$ is the hour and $M$ is the minute.

Step 1: Substitute the values $H=3$, $M=25$.

Answer:

The angle between the hour and minute hand at 3:25 is $47.5°$.

Quick Tip:

The formula $\theta =\left|\frac{11M}{2}-30H\right|$ is derived from the fact that the minute hand moves at $6°$ per minute and the hour hand moves at $0.5°$ per minute, giving a relative speed of $5.5°$ per minute.

Understanding:

We need to rank five friends by their marks using the given inequalities.

Step 1: Write the inequalities from the first statement.

Step 2: Write the inequality from the second statement.

Step 3: Combine both chains.

Step 4: Identify the highest scorer.

R is at the top of the chain, so R scored the highest.

Answer:

R scored the highest marks.

Quick Tip:

Always chain all inequalities into a single sequence to avoid confusion. This also instantly reveals both the highest and lowest scorers.

Understanding:

We need to find the largest of 5 consecutive odd numbers whose average is 35.

Formula:

For consecutive odd numbers, the middle (3rd) number equals the average.

Step 1: Identify the middle number.

Step 2: List the 5 consecutive odd numbers.

Consecutive odd numbers differ by $2$.

Step 3: Verify the average.

Step 4: Identify the largest number.

Answer:

The largest of the five consecutive odd numbers is 39.

Quick Tip:

For any odd count of evenly spaced numbers, the average equals the middle term. This shortcut applies to both consecutive integers and consecutive odd/even numbers.

Understanding:

We need to find $40\%$ of a number, given that the number minus $25\%$ of itself equals $60$.

Formula:

Step 1: Simplify and solve for $x$.

Step 2: Find $40\%$ of $x$.

Answer:

$40\%$ of the number is 32.

Quick Tip:

Subtracting $25\%$ from a number leaves $75\%$ of it. Setting $75\%=60$ immediately gives the original number as $\frac{60\times 100}{75}=80$, which is faster than the algebraic route.