UPPSC (UP) - MCQ Practice Questions

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.