Q&A: practice questions with answers

Concept: Same distance → time is inversely proportional to speed.

1. Distance $=66\times 3=198\text{km}$.
2. Malaika's time $=\frac{198}{99}=2$ hours.

Trick: Speed ratio $66:99=2:3$ → time ratio $3:2$; Arjun $3$ h → Malaika $2$ h.

Answer: (A) 2 hours

Concept: Two successive discounts $a\%$, $b\%$ give less than $(a+b)\%$; the gap is $\frac{ab}{100}\%$ of the price.

1. Successive: $48000\times 0.93\times 0.90=40176$.
2. Flat $17\%$: $48000\times 0.83=39840$.
3. Difference $=40176-39840=336$.

Trick: Gap $=\frac{7\times 10}{100}=0.7\%$ of $48000=336$.

Answer: (D) ₹$336$

Concept: Angle sum of a triangle is ${180}^{\circ }$; an exterior angle equals the sum of the two interior opposite angles.

1. In right $△BDC$: $\angle C={180}^{\circ }-{90}^{\circ }-{60}^{\circ }={30}^{\circ }$.
2. In $△AEC$, $\angle AEB$ is the exterior angle at $E$.
3. $\angle AEB=\angle EAC+\angle ACE={20}^{\circ }+{30}^{\circ }={50}^{\circ }$.

Trick: Perpendicular gives $\angle C={90}^{\circ }-{60}^{\circ }$; then add ${20}^{\circ }$.

Answer: (B) ${50}^{\circ }$

Concept: Number to add $=\text{divisor}-\text{remainder}$.

1. $23\times 3090=71070$, so $71079÷23$ leaves remainder $9$.
2. Number to add $=23-9=14$.
3. Check: $71079+14=71093=23\times 3091$ ✓.

Trick: $71070$ is a multiple of $23$ ($23\times 309\times 10$); remainder is just $9$.

Answer: (D) $14$

Concept: Profit share $\propto$ capital $\times$ time.

1. $M+N=7696$, $M-N=962$ → M's share $=4329$, N's share $=3367$.
2. If N invests $x$: $\frac{3(x+24000)}{4x}=\frac{4329}{3367}$.
3. $10101x+242424000=17316x$ → $7215x=242424000$ → $x=33600$.
4. M's capital $=33600+24000=57600$.

Trick: Check option (D): M $=57600$, N $=33600$ → $57600\times 3:33600\times 4=172800:134400=9:7$; $7696\times \frac{9-7}{16}=962$ ✓.

Answer: (D) ₹$57,600$

Concept: Working together, the hourly rates add: $\frac{1}{T}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$.

1. $\frac{1}{19}+\frac{1}{21}+\frac{1}{8}=\frac{168+152+399}{3192}=\frac{719}{3192}$ (LCM $=3192$).
2. $T=\frac{3192}{719}$ hours.
3. $3192=4\times 719+316$ → $T=4\frac{316}{719}$ hours.

Trick: Together time is less than the fastest pipe alone ($8$ h) → only $4\frac{316}{719}$ is possible.

Answer: (A) $4\frac{316}{719}$ hours

Concept: Divisible by 3 if the digit sum is divisible by 3; by 2, 6, 10 only if the number is even (10 needs last digit 0).

1. Digit sum $=9+3+4+7+2+5=30$, divisible by $3$ ✓.
2. Last digit $5$ is odd → not divisible by $2$, $6$ or $10$.

Trick: An odd number can never be divisible by 2, 6 or 10 – eliminate them at sight.

Answer: (D) $3$

Concept: Take CP $=100$ and follow the markup and discount.

1. List price $=150$; SP $=150\times 0.7=105$.
2. Profit $=105-100=5$ units $=175$ → 1 unit $=35$.
3. List price $=150\times 35=5250$.

Trick: Profit $\%=150\times 0.7-100=5\%$; list price is $30$ times the profit: $175\times 30=5250$.

Answer: (B) $5,250$

Concept: Mean proportional of $a$ and $b$ $=\sqrt{ab}$.

1. $\sqrt{22\times 88}=\sqrt{1936}$.
2. $=44$ (since $88=4\times 22$, $\sqrt{22\times 4\times 22}=2\times 22$).

Trick: If $b=4a$, mean proportional $=2a$.

Answer: (B) $44$

Concept: Product of two numbers $=\text{HCF}\times \text{LCM}$.

1. Other number $=\frac{11\times 495}{55}$.
2. $=\frac{5445}{55}=99$.

Trick: Other number must be a multiple of HCF $11$ – only $99$ qualifies among options.

Answer: (A) $99$

Concept: Place the fixed clues first (positions 1–7 from the left, all facing north).

1. Three people to the left of R → R at position 4.
2. Only A to the right of C → C at 6, A at 7.
3. Three people between C and Q → Q at 2.
4. Left seats 1, 3, 5 with D … B … P → D 1, B 3, P 5. Between D and P: Q, B, R = 3.

Trick: Between positions 1 and 5 there are always $5-1-1=3$ persons.

Answer: (D) Three

Concept: A letter common to two words gets the digit common to both codes.

1. PICK → 3517 and COST → 2146.
2. Common letter: C. Common digit: 1.
3. So C = 1.

Trick: Match common letters with common digits – no need to decode the rest.

Answer: (B) $1$

Concept: Decode each symbol from left to right and draw a family tree.

1. C − O: C is the wife of O.
2. O @ M: O is the father of M → C is the mother of M.
3. M # B: M is the mother of B; B % U: B is the brother of U → M is U's mother.
4. C is the mother of U's mother.

Trick: Wife of the father = mother; go one generation at a time.

Answer: (B) Mother's mother

Concept: Swap the signs first, then apply BODMAS.

1. After swapping: $2\times 8-84÷7+27$.
2. $=16-12+27$.
3. $=31$.

Trick: Rewrite the whole expression with new signs before calculating.

Answer: (B) $31$

Concept: A letter common to two words gets the digit common to both codes.

1. CURE → 8426 and THOU → 5183.
2. Common letter: U. Common digit: 8.
3. So U = 8.

Trick: Common letter ↔ common digit.

Answer: (C) $8$

Concept: Find the position rule: LUNG (1 2 3 4) → UNLG (2 3 1 4) → GNUL (reverse of LUNG).

1. FERN → ERFN (2 3 1 4) and NREF (reverse) ✓.
2. COIR → OICR (2 3 1 4) and RIOC (reverse of COIR) ✓.
3. SWAP → SAWP fails (2nd group should be WASP); BAKE → AKBE ok but AKEB ≠ EKAB; CUTS → UCTS fails.

Trick: Check the easy part first: the third group must be the first group written backwards.

Answer: (A) COIR - OICR - RIOC

Concept: Write letter positions and check the gaps.

1. RUO: 18, 21, 15 → $+3$, $-6$.
2. ILF: 9, 12, 6 → $+3$, $-6$; LOI: 12, 15, 9 → $+3$, $-6$.
3. ORK: 15, 18, 11 → $+3$, $-7$ ✗.

Trick: First-to-third letter gap: R→O, I→F, L→I are all $-3$; O→K is $-4$.

Answer: (A) ORK

Concept: Draw the least-overlap Venn diagram and test each conclusion.

1. Laptops lie inside Computers; some Laptops are Desktops.
2. The Laptop–Desktop common part is also inside Computers → Some computers are desktops ✓ (I).
3. 'Some laptops are desktops' converts to 'Some desktops are laptops' ✓ (II).

Yaad rakhein: 'Some A are B' always gives 'Some B are A'; All + Some (common middle) gives a definite 'Some'.

Answer: (C) Both Conclusions I and II follow

Concept: Replace each sign with its meaning, then apply BODMAS.

1. New expression: $36-48÷4+5\times 3$.
2. $=36-12+15$.
3. $=39$.

Trick: Do ÷ and × first: $12$ and $15$; then $36-12+15$.

Answer: (A) $39$

Concept: Check the differences of the known terms.

1. $142-118=24$, $174-142=32$, $214-174=40$ → differences rise by $8$.
2. So earlier differences are $8$ and $16$.
3. $94+8=102$; check $102+16=118$ ✓.

Trick: Differences $8,16,24,32,40$ are multiples of $8$.

Answer: (A) $102$