Q&A: practice questions with answers

Concept: Translate the words into an equation and solve.

1. Let the number be $x$: $3x-24=258$
2. $3x=282$
3. $x=94$

Trick: Check: $3\times 94=282$, $282-24=258$ ✔

Answer: (A) 94

Concept: Area of rectangle $=l\times b$; area of circle $=\pi r^2$; circumference $=2\pi r$.

1. $169\times 154=26026{\text{m}}^2$
2. $\frac{22}{7}{r}^2=26026\Rightarrow r^2=8281\Rightarrow r=91$
3. $2\pi r=2\times \frac{22}{7}\times 91=572\text{m}$

Trick: $154=22\times 7$, so $r^2=169\times 49\Rightarrow r=13\times 7=91$ instantly.

Answer: (C) 572

Concept: Find each root by prime factorisation / known powers.

1. $\sqrt[6]{729}=\sqrt[6]{3^6}=3$
2. $\sqrt[4]{65536}=\sqrt[4]{{16}^4}=16$
3. $\sqrt[3]{5832}=18$ (as ${18}^3=5832$)
4. $\sqrt{1764}=42$; sum $=3+16+18+42=79$

Trick: $65536=2^{16}$, so its 4th root is $2^4=16$.

Answer: (D) 79

Concept: $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$; use the remaining distance and remaining time.

1. Covered: $\frac{2}{3}\times 387=258\text{km}$ in $\frac{5}{7}\times 21=15\text{h}$
2. Left: $387-258=129\text{km}$ in $21-15=6\text{h}$
3. Speed $=\frac{129}{6}=21.5\text{km/h}$

Trick: Remaining distance $=\frac{1}{3}$, remaining time $=\frac{2}{7}$ of total.

Answer: (A) 21.5

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

1. $SI=\frac{350\times 20\times 1.5}{100}$
2. $=\frac{10500}{100}=105$

Trick: 20% per year for 1.5 years = 30% of ₹350 = ₹105.

Answer: (C) ₹105

Concept: Empirical relation: $\text{Mode}=3\text{Median}-2\text{Mean}$.

1. $2\text{Mean}=3\times 65-52.7=195-52.7=142.3$
2. $\text{Mean}=71.15\approx 71.2$

Trick: $\text{Mean}=\frac{3\text{Median}-\text{Mode}}{2}$

Answer: (A) 71.2

Concept: Mean proportional of $a$ and $b$ is $\sqrt{ab}$, i.e. $m^2=ab$.

1. ${68}^2=272x$
2. $4624=272x$
3. $x=17$

Trick: $272=4\times 68$, so $x=\frac{68}{4}=17$.

Answer: (A) 17

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

1. Total parts $=6+59+41=106$
2. 1 part $=\frac{3180}{106}=30$
3. $Y-Z=(59-41)\times 30=18\times 30=540$

Trick: Find the value of 1 part, then multiply by the difference of parts.

Answer: (D) ₹540

Concept: Work done $=\text{rate}\times \text{time}$; A’s rate $=\frac{1}{25}$, B’s rate $=\frac{1}{18}$ per day.

1. A in 4 days: $\frac{4}{25}$
2. Remaining: $1-\frac{4}{25}=\frac{21}{25}$
3. B’s time $=\frac{21}{25}\times 18=\frac{378}{25}=15\frac{3}{25}$ days

Trick: Remaining work × B’s total days = B’s time.

Answer: (A) $15\frac{3}{25}$

Concept: Correct sum = wrong sum − wrong value + right value.

1. Wrong sum $=10\times 40=400$
2. Correct sum $=400-33+50=417$
3. Correct average $=\frac{417}{10}=41.7$

Trick: Change in average $=\frac{50-33}{10}=1.7$ → $40+1.7$.

Answer: (D) 41.7

Concept: Net change $=a+b+\frac{ab}{100}$.

1. $a=-16$, $b=+10$
2. $-16+10+\frac{(-16)(10)}{100}=-6-1.6=-7.6\%$
3. So the final salary is 7.6% lower.

Trick: Check: $100\times 0.84\times 1.1=92.4$.

Answer: (D) 7.6%

Concept: For 2 years: $CI-SI=P{\left(\frac{R}{100}\right)}^2$.

1. $=17700\times {\left(\frac{4}{100}\right)}^2$
2. $=17700\times \frac{16}{10000}=28.32$

Trick: 2-year difference = interest on first year’s interest.

Answer: (B) ₹28.32

Concept: Stream speed $=\frac{\text{Downstream}-\text{Upstream}}{2}$.

1. Upstream $=\frac{184}{48}=\frac{23}{6}\text{km/h}$
2. Downstream $=\frac{184}{12}=\frac{46}{3}\text{km/h}$
3. Stream $=\frac{1}{2}(\frac{92}{6}-\frac{23}{6})=\frac{69}{12}=5.75\text{km/h}$

Trick: Same distance: stream $=\frac{d}{2}(\frac{1}{t_1}-\frac{1}{t_2})=92(\frac{1}{12}-\frac{1}{48})$.

Answer: (D) 5.75 km/hr

Concept: For a fixed selling amount, $\text{SP of }n\text{ items}=1.4\times \text{CP of }n\text{ items}$ when gain is $40\%$.

1. CP of 1 lemon = ₹$\frac{1}{7}$.
2. For 40% gain, SP of 1 lemon $=\frac{1}{7}\times \frac{140}{100}$ = ₹$\frac{1}{5}$.
3. So for ₹1 he must sell $1÷\frac{1}{5}=5$ lemons.

Trick: Lemons to sell $=\frac{7\times 100}{140}=5$.

Answer: (C) 5

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

1. In $△ABC$: $\angle BCA={180}^{\circ }-{69}^{\circ }-{23}^{\circ }={88}^{\circ }$.
2. $BC\parallel AD$, so $\angle CAD=\angle BCA={88}^{\circ }$ (alternate angles).
3. $AC=CD$, so $\angle CDA=\angle CAD={88}^{\circ }$.
4. In $△ACD$: $\angle ACD={180}^{\circ }-{88}^{\circ }-{88}^{\circ }=4^{\circ }$.

Trick: $\angle ACD={180}^{\circ }-2({180}^{\circ }-{69}^{\circ }-{23}^{\circ })={180}^{\circ }-{176}^{\circ }=4^{\circ }$.

Answer: (A) $4^{\circ }$

Concept: $\text{Average}=\frac{\text{Sum}}{\text{Count}}$.

1. First 10 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
2. Sum $=2+3+5+7+11+13+17+19+23+29=129$.
3. Average $=\frac{129}{10}=12.9$.

Yaad rakhein: Sum of first 10 primes = 129; of first 25 primes (up to 100) = 1060.

Answer: (D) 12.9

Concept: The largest cone cut from a cube of edge $a$ has $r=\frac{a}{2}$ and $h=a$; $V=\frac{1}{3}\pi r^{2}h$.

1. $a=8$, so $r=4\text{cm}$, $h=8\text{cm}$.
2. $V=\frac{1}{3}\times \frac{22}{7}\times 4^2\times 8=\frac{22\times 128}{21}=\frac{2816}{21}$.
3. $\frac{2816}{21}=134\frac{2}{21}{\text{cm}}^3$.

Trick: Largest cone in cube $=\frac{\pi a^3}{12}=\frac{22\times 512}{84}=134\frac{2}{21}$.

Answer: (B) $134\frac{2}{21}$

Concept: Follow BODMAS – innermost bracket first.

1. $(1-5+4)=0$.
2. $7\times 0=0$, and $0÷91=0$.
3. $127-0=127$.

Trick: Spot the zero bracket – the whole term vanishes.

Answer: (C) 127

Concept: Net rate = filling rate − emptying rate.

1. Net rate per minute $=\frac{1}{21}-\frac{1}{24}=\frac{8-7}{168}=\frac{1}{168}$ of the tank.
2. Full tank takes 168 minutes together.
3. One-fourth tank takes $\frac{168}{4}=42$ minutes.

Trick: LCM method: tank = 168 units; filler 8, emptier 7 units per minute → net 1 unit; $\frac{1}{4}$ tank = 42 units = 42 min.

Answer: (A) 42

Concept: A product stays the same if the total shift of decimal points is zero.

1. Option (C): $6893.5\to 68.935$ (divided by ${10}^2$), $603.3\to 6033$ (×10), $0.3019\to 3.019$ (×10).
2. Net factor $=\frac{10\times 10}{100}=1$ → product unchanged ✓.
3. (A) and (B) give a net factor $\frac{1}{100}$; (D) gives 100.

Trick: Count decimal places: original 1 + 1 + 4 = 6; in (C) 3 + 0 + 3 = 6 – same total.

Answer: (C) $68.935\times 6033\times 3.019$