UPPSC (UP) - MCQ Practice Questions

Understanding:

We need to find the average speed for a round trip where the two speeds are different.

Formula:

For equal distances, the average speed is the harmonic mean of the two speeds:

Step 1: Substitute the values.

Answer:

The average speed for the entire journey is $48$ km/h.

Quick Tip:

Never use the arithmetic mean of speeds when the distances are equal — the harmonic mean is always less than the arithmetic mean ($50$ km/h here). The arithmetic mean applies only when the times are equal.

Understanding:

We need to find the coding rule applied to 'MANGO' → 'OCPIQ' and apply it to 'GRAPE'.

Step 1: Find the shift for each letter.

M → O: M is the 13th letter, O is the 15th. Shift = +2

A → C: A is the 1st, C is the 3rd. Shift = +2

N → P: N is the 14th, P is the 16th. Shift = +2

G → I: G is the 7th, I is the 9th. Shift = +2

O → Q: O is the 15th, Q is the 17th. Shift = +2

Step 2: The rule is — each letter is shifted forward by 2 positions in the alphabet.

Step 3: Apply the rule to 'GRAPE'.

G → I

R → T

A → C

P → R

E → G

So 'GRAPE' is coded as 'ITCRG'.

Step 4: Re-check letter by letter.

G(7)+2=9=I ✓, R(18)+2=20=T ✓, A(1)+2=3=C ✓, P(16)+2=18=R ✓, E(5)+2=7=G ✓

The coded word is ITCRG — which matches option A: ITCRI...

Step 5: Re-examine option A carefully: ITCRI vs computed ITCRG.

Option A: I-T-C-R-I, Option computed: I-T-C-R-G.

E(5)+2=G(7). So the last letter must be G.

Option A ends in I, which does not match. Re-examining: none of the options exactly match ITCRG except we must recheck.

G→I, R→T, A→C, P→R, E→G → ITCRG.

Option A: ITCRI — last letter I ≠ G.

Option B: ITCRF — last letter F ≠ G.

Option C: HSCQF — does not match.

Option D: IUCRG — second letter U ≠ T.

The closest correct derivation gives ITCRG. Option D has the correct last letter G but wrong second letter (U instead of T). The correct derived answer ITCRG is closest to option A with only the last letter differing, suggesting a typo in option A. Since no option matches perfectly and option A is the closest with 4 of 5 letters correct, and option D has the correct terminal letter G with R(18)+2≠U, the intended answer based on standard exam practice is option A.

Answer:

Applying the +2 shift rule: G→I, R→T, A→C, P→R, E→G gives ITCRG.

Understanding:

We need to trace the blood relationships step by step to find how D is related to A.

Step 1: Establish the relationships.

Step 2: Determine D's relation to A.

Since C is A's sibling (brother/sister) and C is the father of D, D is the child of A's sibling.

A child of one's sibling is a Nephew (if male) or Niece (if female).

Step 3: Determine A's relation to D.

From A's perspective, D is A's sibling's child → D is A's Nephew or Niece.

From D's perspective, A is D's parent's sibling → A is D's Uncle.

Answer:

D is the Nephew or Niece of A.

Quick Tip:

In blood relation problems, always build a family tree step by step — it avoids confusion between 'how is D related to A' and 'how is A related to D'.

Understanding:

We need to find the net profit percentage when a markup and a discount are both applied.

Formula:

Let the cost price be $\text{CP}=100$ (assumed).

Step 1: Find the Marked Price.

Step 2: Find the Selling Price after discount.

Step 3: Calculate Profit Percentage.

Answer:

The shopkeeper's profit percentage is $12.5\%$.

Quick Tip:

Use the combined formula: $\text{Net}\%=x+y+\frac{xy}{100}$ where $x=+25\%$ and $y=-10\%$: $25-10-\frac{250}{100}=15-2.5=12.5\%$. This is faster in exams.

Understanding:

We need to identify the pattern in the series and find the next term.

Step 1: Find the differences between consecutive terms.

The differences are $4,8,16,32$ — each difference doubles.

Step 2: The next difference should be $32\times 2=64$.

Step 3: Find the next term.

Verification:

Each term follows the rule: ${\text{Term}}_n=2^{n+1}-1$.

Answer:

The missing number is $127$.

Quick Tip:

Whenever a series looks like $2^n-1$, verify by checking if each term equals the previous term doubled plus one: $2\times 63+1=127$. This shortcut works for all such geometric-difference series.

Understanding:

We need to trace the relationship described to identify how the woman in the photo is related to the man.

Step 1: Decode 'only son of my grandfather'.

The man's grandfather's only son is the man's father (assuming the man is the only son, or more precisely the subject is referring to his own father as the only son of grandfather).

Step 2: Decode 'daughter of the only son of my grandfather'.

The daughter of the man's father is the man's sister.

Step 3: Conclusion.

The woman in the photograph is the daughter of the man's father, which makes her the man's sister.

Answer:

The woman in the photograph is the man's Sister.

Quick Tip:

In such questions, always resolve the phrase from the innermost relationship outward. 'Only son of grandfather' = father; 'daughter of father' = sister.

Understanding:

We need to find the time taken to fill the tank when one pipe fills and the other empties simultaneously.

Formula:

Step 1: Calculate the net rate of filling per hour.

Step 2: Find the total time to fill the tank.

Answer:

The tank will be filled in $36$ hours.

Quick Tip:

When a fill pipe is faster than an empty pipe, the tank will eventually fill. If the empty pipe were faster, the tank would never fill — always check which rate is larger before solving.

Understanding:

We need to find the total number of students in the row using position data before and after interchange.

Step 1: After interchange, Ramesh takes Suresh's original position.

So Ramesh's new position from the left ($18$th) is Suresh's original position from the left.

This means Suresh was originally $18$th from the left.

Step 2: Use Suresh's positions to find the total.

Suresh is $18$th from the left and $10$th from the right.

Verification:

Ramesh is $14$th from left; after interchange he goes to Suresh's position ($18$th from left) ✓. Suresh moves to $14$th from left, which is $(27-14+1)=14$th from right — consistent.

Answer:

The total number of students in the row is $27$.

Quick Tip:

The key insight: after interchange, Ramesh occupies Suresh's old position. So Suresh's position from the left equals Ramesh's new position from the left ($18$). Then apply Total $=$ Left $+$ Right $-1$.

Understanding:

We first find the principal from the SI data, then compute the CI.

Formula:

Step 1: Find the Principal.

Step 2: Calculate Compound Interest for $2$ years.

Answer:

The compound interest for $2$ years is $\text{Rs.}1050$.

Quick Tip:

For 2-year CI, a quick formula is $\text{CI}=P\left(\frac{R}{100}\right)\left(2+\frac{R}{100}\right)$. Here: $5000\times 0.1\times 2.1=1050$. This saves squaring time in exams.

Understanding:

We need to arrange six friends in a row using the given clues and identify who sits at the left end.

Step 1: Place D and C using 'D is second from the left' and 'C is immediately right of D'.

Position: _ D C _ _ _

(D is at position 2, C is at position 3)

Step 2: F is at one end (either position 1 or position 6).

If F is at position 1, then position 1 = F.

But then B is immediately left of F — impossible (nothing to the left of position 1).

So F is at position 6 (right end).

Position: _ D C _ _ F

Step 3: B is immediately left of F → B is at position 5.

Position: _ D C _ B F

Step 4: E is between A and B. The remaining positions are 1 and 4.

E must be between A and B. B is at position 5. For E to be between A and B:

If E is at position 4, A must be at position 3 or further left, and B at position 5 — but position 3 is C.

So A is at position 1 and E is at position 4: arrangement is A D C E B F.

Check: E(4) is between A(1)... actually 'between' means E is flanked by A and B.

With A at 1, E at 4, B at 5: E is immediately left of B but A is not adjacent to E.

Step 5: Re-examine. Remaining positions are 1 and 4 for A and E.

If E=4, A=1: sequence A D C E B F. E is at 4, neighbours are C(3) and B(5). E is between C and B, not A and B — doesn't satisfy the condition.

If A=4, E=1: sequence E D C A B F. E is at 1, A is at 4, B at 5. A is between C(3) and B(5) ✓, but E is not between A and B.

Try: E must be directly between A and B (consecutive positions). A and B must be on either side of E.

With B at 5: E at 4, A at 3 — but position 3 = C. Contradiction.

So the only valid option: A at 1, E at 4, reading E between positions (A far left, then E, then B): in the row A D C E B F, E is sandwiched between C and B adjacently, but E is between A and B in the broader sense (A...E...B in left-to-right order). This is the intended interpretation in such exam questions.

Step 6: Final arrangement: A D C E B F.

The person at the left end (position 1) is A.

Answer:

A is sitting at the left end of the row.

Quick Tip:

In linear arrangement puzzles, always fix the anchored positions first (here D's position and the ends), then place the remaining clues. The phrase 'E is between A and B' in Indian competitive exams usually means A…E…B in order, not necessarily adjacent.