Q&A: practice questions with answers

Concept: Curved surface area of a cylinder $=2\pi rh$.

1. $2\times \frac{22}{7}\times r\times 16=2200$
2. $\frac{704}{7}r=2200\Rightarrow r=\frac{2200\times 7}{704}=\frac{15400}{704}$
3. $r=21.875\approx 21.88\text{cm}$

Trick: $\frac{2200}{2\pi h}$: $2\pi \times 16\approx 100.57$, and $2200÷100.57\approx 21.9$ → 21.88.

Answer: (B) 21.88

Concept: Walk one way + drive one way = 5.5 h; drive both ways = 5.5 − 3 = 2.5 h.

1. One-way drive $=\frac{2.5}{2}=1.25$ h
2. One-way walk $=5.5-1.25=4.25$ h
3. Walk both ways $=2\times 4.25=8.5$ h $=8$ h $30$ min

Trick: Walk both ways $=2\times (\text{mixed})-(\text{drive both})=11-2.5=8.5$ h.

Answer: (B) 8 hours 30 minutes

Concept: If SP of $a$ articles = CP of $b$ articles and $b<a$, it is a loss of $\frac{a-b}{a}\times 100\%$.

1. Let CP of 1 book = ₹1 → SP of 50 books = ₹19, CP of 50 books = ₹50
2. Loss $=50-19=31$
3. Loss% $=\frac{31}{50}\times 100=62\%$

Trick: SP side has more items (50 > 19) → loss; divide by the SP-side count (50).

Answer: (C) 62% loss

Concept: Average $=\frac{\text{sum}}{\text{count}}$.

1. Sum $=40+49+56+74+36=255$
2. Average $=\frac{255}{5}=51$

Trick: Take 50 as base: deviations $-10,-1,+6,+24,-14$ sum to $+5$ → $50+\frac{5}{5}=51$.

Answer: (C) 51

Concept: Rule out options by quick tests, then divide.

1. Odd number → not divisible by 36 or 50 (50 needs last digit 0)
2. $861616843÷43$: $43\times 20037601=861616843$ exactly
3. (Check 47: remainder is not 0.)

Trick: Break it: $860000000=43\times 20000000$; remainder part $1616843=43\times 37601$.

Answer: (A) 43

Concept: $SI=\frac{P\times R\times T}{100}$.

1. $SI=\frac{400\times 16\times 5.5}{100}$
2. $=4\times 16\times 5.5=64\times 5.5=352$

Trick: Interest per year $=64$; $5.5$ years → $64\times 5+32=352$.

Answer: (C) ₹352

Concept: Take total work = LCM of days; efficiency = work ÷ days.

1. Work $=\text{LCM}(11,15)=165$; Lokesh $=15$/day, Manoj $=11$/day
2. 5 days together: $5\times 26=130$
3. Left $=165-130=35$; Lokesh alone $=\frac{35}{15}=\frac{7}{3}=2\frac{1}{3}$ days

Trick: Fraction way: $5(\frac{1}{11}+\frac{1}{15})=\frac{26}{33}$; remaining $\frac{7}{33}\times 11=\frac{7}{3}$.

Answer: (A) $2\frac{1}{3}$

Concept: Together time $=\frac{1}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}$.

1. LCM$(11,26,12)=1716$ units
2. Per hour: A $=156$, B $=66$, C $=143$ → total $365$
3. Time $=\frac{1716}{365}=4\frac{256}{365}$ hours

Trick: Time must be less than the fastest pipe (11 h) alone and roughly $\frac{1716}{365}\approx 4.7$, so only option (D).

Answer: (D) $4\frac{256}{365}$ hours

Concept: Average speed $=\frac{\text{total distance}}{\text{total time}}$.

1. Times: $\frac{252}{63}=4$, $\frac{891}{99}=9$, $\frac{183}{61}=3$ → total $16$ h
2. Distance $=252+891+183=1326$ km
3. Average $=\frac{1326}{16}=82.875\approx 82.88\text{km/h}$

Trick: Never average the speeds directly; each leg here divides exactly, so add times.

Answer: (C) 82.88

Concept: Extra expenses (overheads) are added to CP; Profit% $=\frac{\text{Profit}}{\text{CP}}\times 100$.

1. Effective CP $=199+9=₹208$; SP $=₹231$
2. Profit $=231-208=₹23$
3. Profit% $=\frac{23}{208}\times 100=\frac{2300}{208}=\frac{575}{52}\%$

Trick: Always add repair/decoration cost to CP before finding profit%.

Answer: (C) $\frac{575}{52}\%$ profit

Concept: Fix definite positions first (number positions 1 = bottom to 7 = top).

1. B = 2; three boxes between B and E → E = 6
2. C below B → C = 1
3. Only A between E and F → A = 5, F = 4 (above E is impossible)
4. G above E → G = 7; D takes the last place 3
5. Between C (1) and D (3): only B → 1 box

Trick: Boxes between positions p and q = |p − q| − 1 = 3 − 1 − 1 = 1.

Answer: (C) 1

Concept: Replace letters by signs and follow BODMAS.

1. $99÷9+12\times 2-16$
2. $=11+24-16=19$

Trick: Divide and multiply first: $11$ and $24$, then $35-16$.

Answer: (D) 19

Concept: Facing the centre: left = clockwise, right = anticlockwise.

1. Place I; V is immediate left of I; W is third to the left of I
2. J is second to the left of K and H is immediate left of J → only fit: K, J, H in the remaining seats as shown
3. U takes the last seat (immediate right of I)
4. Third to the right of U: U → H → J → W

Trick: In a 7-seat circle, 3rd to the right = 4th to the left — use whichever is shorter to check.

Answer: (A) W

Concept: Track each letter position separately.

1. 1st letters: Z, V, R, N → −4 each → J
2. 2nd: W, S, O, K → −4 → G
3. 3rd: R, N, J, F → −4 → B

Trick: All three positions move −4: shift NKF back by 4 → JGB.

Answer: (A) JGB

Concept: Each position moves +8 (wrapping after Z).

1. 1st: G, O, W, E (W+8 wraps to E) → E+8 = M
2. 2nd: D, L, T, B → B+8 = J
3. 3rd: B, J, R, Z → Z+8 = H

Trick: Z+8: count past Z → A(1)… H(8).

Answer: (D) MJH

Concept: “Only A above D” fixes the top two; “only B below G” fixes the bottom two.

1. A = 7 (top), D = 6
2. Only E between D and F → E = 5, F = 4
3. B = 1 (bottom), G = 2; C = 3
4. Below F (4): C, G, B → 3 boxes

Trick: ‘Only X above Y’ means X is on top and Y just below it.

Answer: (A) 3

Concept: Check gaps between alphabet positions.

1. QJM: 17, 10, 13 → −7, +3
2. WPS: 23, 16, 19 → −7, +3; SLO: 19, 12, 15 → −7, +3
3. UNR: 21, 14, 18 → −7, +4 ✗

Trick: First gap is −7 in all; the second gap decides the odd one.

Answer: (A) UNR

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

1. 5 % % → the first % counts
2. 4 £ & → £ counts
3. 1 * (end) → nothing follows, does not count; other symbols are not preceded by a number

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

Answer: (D) 2

Concept: A word common to two sentences takes the code common to both.

1. ‘life’ is in both sentences
2. Common code in ‘tu ro na’ and ‘ko ie na’ is ‘na’

Trick: Common word ↔ common code.

Answer: (D) na

Concept: Compare alphabet-position gaps.

1. IEK: 9, 5, 11 → −4, +6; LHN: 12, 8, 14 → −4, +6
2. FBH: 6, 2, 8 → −4, +6
3. NJO: 14, 10, 15 → −4, +5 ✗

Trick: Middle letter is 4 behind the first and 6 behind the last in the group.

Answer: (C) NJO