Q&A: practice questions with answers

Concept: Profit is shared in the ratio of investments (same time).

1. Total ratio $=3+53+24=80$ parts; 1 part $=\frac{1280}{80}=16$
2. Difference of Q and R $=53-24=29$ parts
3. $29\times 16=464$

Trick: Find the difference in parts first, multiply only once.

Answer: (B) ₹464

Concept: $\text{SP}=\text{CP}\times \frac{100+P\%}{100}$ and $\text{MP}=\text{SP}\times \frac{100}{100-D\%}$.

1. $\text{SP}=576\times \frac{115}{100}=662.4$
2. $\text{MP}=662.4\times \frac{100}{96}=690$

Trick: Directly: $\text{MP}=576\times \frac{115}{96}=6\times 115=690$ (since $576=96\times 6$).

Answer: (B) ₹690

Concept: If the whole and one part have the same rate, the other part must have that rate too.

1. Females $=373000-227000=146000$
2. Literate total $=0.69\times 373000$; literate males $=0.69\times 227000$
3. Literate females $=0.69\times (373000-227000)=0.69\times 146000$ → $69\%$

Trick: Overall 69% and males 69% ⇒ females also 69% – no calculation needed.

Answer: (B) 69%

Concept: Form two equations in pen price $x$ and pencil price $y$ and solve.

1. $18x+4y=200$ … (i)
2. $19(x-1)+3(y+3)=151\Rightarrow 19x+3y=161$ … (ii)
3. $4\times$(ii): $76x+12y=644$; $3\times$(i): $54x+12y=600$ → $22x=44$, $x=2$, $y=41$
4. $12x+10y=24+410=434$

Trick: Make the $y$-coefficients equal (12) and subtract – one step gives $x$.

Answer: (B) ₹434

Concept: If $a\%$ of A $=$ $b\%$ of B, then $A:B=b:a$.

1. $\frac{77}{100}A=\frac{3}{4}B=\frac{75}{100}B$
2. $77A=75B\Rightarrow A:B=75:77$

Trick: Write $\frac{3}{4}$ as 75% and simply swap: $75:77$.

Answer: (A) $75:77$

Concept: Solve innermost bracket first, then multiplication, then addition, then division.

1. $(2-3)=-1$
2. $7\times (-1)=-7$; $17-7=10$
3. $290÷10=29$

Trick: Order: ( ) → { } → [ ].

Answer: (D) 29

Concept: Use ${\sec }^{2}A-{\tan }^{2}A=1$ and the standard result $\frac{\tan A+\sec A-1}{\tan A-\sec A+1}=\sec A+\tan A=\frac{1+\sin A}{\cos A}$.

1. Denominator $=\tan A+\sec A-1$.
2. So $\frac{\tan A-\sec A+1}{\tan A+\sec A-1}=\frac{\cos A}{1+\sin A}$.
3. Expression $=(1+\sin A)\sec A\times \frac{\cos A}{1+\sin A}=\sec A\cos A=1$

Trick: Test $A={45}^{\circ }$: numerator $=(1+\frac{1}{\sqrt{2}})(2-\sqrt{2})\sqrt{2}=\sqrt{2}$ and denominator $=\sqrt{2}$, so the value is 1.

Answer: (B) 1

Concept: Net rate $=$ sum of filling rates − emptying rate (in tank per minute).

1. $\frac{1}{70}+\frac{1}{30}-\frac{1}{x}=\frac{1}{28}$
2. LCM 420: $\frac{6+14}{420}-\frac{1}{x}=\frac{15}{420}$
3. $\frac{1}{x}=\frac{5}{420}=\frac{1}{84}$ → $x=84$ min

Trick: Take capacity $=420$ units: fillers $6+14=20$/min, net $15$/min ⇒ leak $=5$/min ⇒ $\frac{420}{5}=84$ min.

Answer: (B) 84 min

Concept: Angle sum of a triangle is ${180}^{\circ }$; with parallel lines, alternate angles are equal; equal sides face equal angles.

1. In $△ABC$: $\angle BCA={180}^{\circ }-{40}^{\circ }-{120}^{\circ }={20}^{\circ }$
2. $BC\parallel AD$ ⇒ $\angle CAD=\angle BCA={20}^{\circ }$ (alternate angles)
3. $AC=CD$ ⇒ $\angle CDA=\angle CAD={20}^{\circ }$
4. $\angle ACD={180}^{\circ }-{20}^{\circ }-{20}^{\circ }={140}^{\circ }$

Trick: Isosceles triangle with base angle $\theta$ has apex angle ${180}^{\circ }-2\theta$.

Answer: (C) ${140}^{\circ }$

Concept: Let present ages be father $F$, son $S$; translate each statement into an equation.

1. 5 years ago: $F-5=2(S-5)+14\Rightarrow F=2S+9$
2. After $n$ years: $F+n=2(S+n)$
3. $2S+9+n=2S+2n\Rightarrow n=9$

Trick: Father is $9$ years more than twice the son now; that extra 9 disappears after exactly 9 years.

Answer: (A) 9

Concept: Check the letter positions: A=1 … Z=26.

1. WY-PY: W(23)+2=Y; W−7=P; 2nd letter Y repeats.
2. QS-JS: Q+2=S; Q−7=J; S repeats. UW-NW: U+2=W; U−7=N; W repeats.
3. SU-LP: S+2=U, S−7=L, but last letter P ≠ U.

Trick: Here the last letter of both clusters must be the same – SU-LP breaks it.

Answer: (B) SU-LP

Concept: $\text{Total}=\text{rank from top}+\text{rank from bottom}-1$.

1. $23+11-1=33$

Trick: Subtract 1 because the person is counted in both ranks.

Answer: (C) 33

Concept: Look at differences of consecutive terms.

1. Differences: $9,17,25,33$ – they increase by 8.
2. Next difference $=41$
3. $139+41=180$

Trick: When differences grow by a constant, it's a second-order series.

Answer: (B) 180

Concept: Facing the centre: a person's right is anticlockwise and left is clockwise.

1. Fix D; E is to D's immediate right.
2. Counting from E's left (clockwise), 3 people then G – so D, F, I lie between E and G.
3. H has 3 people between it and D → H next to G; F is immediate right of I, X fills the last seat.
4. From I going left: G, H, then X → 2 people between.

Trick: In a 7-seat circle, '3 between' one way means '2 between' the other way – use it to place H quickly.

Answer: (D) Two

Concept: Find the position change of each letter (A=1 … Z=26).

1. KFD → IIB: K−2=I, F+3=I, D−2=B
2. UDD → SGB: U−2=S, D+3=G, D−2=B
3. WBI → UEG: W−2=U, B+3=E, I−2=G ✓

Trick: Rule $(-2,+3,-2)$; others fail the third letter (M→O, B→D, H→K).

Answer: (D) WBI : UEG

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

1. FEAR and THEM share only the letter E.
2. 2461 and 1593 share only the digit 1.
3. So E = 1.

Yaad rakhein: Common letter ↔ common digit.

Answer: (B) 1

Concept: Track each letter position separately.

1. 1st letters: K, M, O, Q, S (+2)
2. 2nd letters: P, O, N, M, L (−1)
3. 3rd letters: X, U, R, O, L (−3)

Trick: Check the last term SLL to confirm all three rules.

Answer: (D) QMO

Concept: Draw the family tree: siblings on one line, couple joined, child below.

1. R, C and A are siblings; R is male (brother).
2. A is the mother of G and G is the son of H ⇒ H is G's father, i.e. A's husband.
3. R is the brother of H's wife.

Trick: Mother + father of the same child ⇒ they are husband and wife.

Answer: (C) Wife's brother

Concept: Write the new order under the old one and compare place by place.

1. Original: 7 6 4 2 9 1 5
2. Ascending: 1 2 4 5 6 7 9
3. Only the 3rd digit (4) is in the same place.

Trick: Sort first, then compare column-wise – don't count digits, count positions.

Answer: (D) One

Concept: Check every symbol for the pattern: even number – symbol – odd number.

1. 8 $ 7 → 8 even, 7 odd ✓
2. 2 # 6 → 6 is even ✗; 6 & * → next is a symbol ✗
3. All other symbols are preceded by an odd number or a symbol ✗

Trick: Scan only the even numbers and look at what follows them – faster than checking each symbol.

Answer: (B) One