Q&A: practice questions with answers

Concept: Total users of each mode $=$ boys $+$ girls; pick the largest.

1. School bus $=80+140=220$; Bicycle $=280+190=470$.
2. Walking $=130+90=220$; Other vehicles $=200+250=450$.
3. Maximum $=470$ (Bicycle).

Trick: Other vehicles has the most girls (250), but bicycle wins on the combined total.

Answer: (A) Bicycle

Concept: Speed in still water $=\frac{\text{downstream}+\text{upstream}}{2}$.

1. Downstream $=\frac{72}{6}=12\text{km/h}$.
2. Upstream $=\frac{72}{12}=6\text{km/h}$.
3. Still water $=\frac{12+6}{2}=9\text{km/h}$.

Trick: Half the difference ($3\text{km/h}$) would be the stream speed – do not confuse.

Answer: (B) 9 km/h

Concept: BODMAS with a bar (vinculum) – solve the bar first, then (), {}.

1. Bar: $2\frac{1}{3}-\frac{1}{3}=2$.
2. $(3\frac{1}{3}÷2)=\frac{10}{3}\times \frac{1}{2}=\frac{5}{3}$.
3. $\{4\frac{1}{3}+\frac{5}{3}\}=\frac{13}{3}+\frac{5}{3}=6$.
4. $5\frac{1}{3}-6=\frac{16}{3}-6=-\frac{2}{3}$.

Trick: Order of brackets: bar $\to$ ( ) $\to$ { } $\to$ [ ].

Answer: (D) $-\frac{2}{3}$

Concept: In numerator and denominator do ÷ and × left to right before + and −.

1. Numerator: $\frac{3}{7}÷\frac{9}{49}\times \frac{3}{14}=\frac{7}{3}\times \frac{3}{14}=\frac{1}{2}$, so $1-\frac{1}{2}=\frac{1}{2}$.
2. Denominator: $\frac{3}{5}÷\frac{1}{25}\times \frac{1}{30}=15\times \frac{1}{30}=\frac{1}{2}$, so $1+\frac{1}{2}=\frac{3}{2}$.
3. Value $=\frac{1/2}{3/2}=\frac{1}{3}$.

Trick: ÷ means multiply by the reciprocal; keep left-to-right order.

Answer: (C) $\frac{1}{3}$

Concept: Chain the percentages from enrolled voters to the winner\'s votes.

1. Let enrolled voters $=N$. Votes cast $=0.8N$; valid $=0.95\times 0.8N=0.76N$.
2. Candidate: $0.8\times 0.76N=0.608N=9500$.
3. $N=\frac{9500}{0.608}=15625$.

Trick: $N\times \frac{4}{5}\times \frac{19}{20}\times \frac{4}{5}=9500\Rightarrow N=9500\times \frac{125}{76}=15625$.

Answer: (C) 15625

Concept: Net filling rate $=\frac{1}{\text{inlet time}}-\frac{1}{\text{outlet time}}$; time $=\frac{ab}{b-a}$.

1. Time $=\frac{3.6\times 6.3}{6.3-3.6}=\frac{22.68}{2.7}$.
2. $=8.4$ hours.

Trick: Scale by 10: $\frac{36\times 63}{27}=84$, then divide by 10.

Answer: (B) 8.4

Concept: Successive gains multiply: $\text{C.P.}\times 1.1\times 1.2=$ final price.

1. $\text{C.P.}\times \frac{11}{10}\times \frac{6}{5}=26400000$.
2. $\text{C.P.}=26400000\times \frac{50}{66}=20000000$.

Trick: Net factor $1.32$: $2.64÷1.32=2$ crore.

Answer: (A) ₹2,00,00,000

Concept: Convert each percentage group to runs using that year\'s total.

1. 2019-20: NZ + Pakistan $=14\%+16\%=30\%$ of $4000=1200$.
2. 2020-21: Sri Lanka + Pakistan $=20\%+15\%=35\%$ of $5000=1750$.
3. Difference $=1750-1200=550$.

Trick: Totals differ year to year, so never subtract percentages directly across the two charts.

Answer: (D) 550

Concept: $V=\frac{4}{3}\pi r^3$, $S=4\pi r^2$.

1. $\frac{4}{3}\pi r^3=\frac{256}{3}\pi \Rightarrow r^3=64$, $r=4\text{cm}$.
2. $S=4\pi \times 16=64\pi {\text{cm}}^2$.

Trick: Shortcut: $S=\frac{3V}{r}=\frac{3}{4}\times \frac{256}{3}\pi =64\pi$.

Answer: (B) $64\pi {\text{cm}}^2$

Concept: Standard values: $\tan {45}^{\circ }=1$, $\sin {60}^{\circ }=\frac{\sqrt{3}}{2}$, $\cos {60}^{\circ }=\frac{1}{2}$, $\cot {30}^{\circ }=\sqrt{3}$.

1. LHS $=k\times 1\times \frac{\sqrt{3}}{2}$.
2. RHS $=\frac{1}{2}\times \sqrt{3}=\frac{\sqrt{3}}{2}$.
3. So $k=1$.

Trick: $\sin {60}^{\circ }=\cos {30}^{\circ }$ and $\cot {30}^{\circ }=\tan {60}^{\circ }$ – both sides are $\frac{\sqrt{3}}{2}$.

Answer: (A) 1

Concept: When both run in the same direction, the gap closes at the relative speed (difference of speeds).

1. Relative speed $=42-30=12\text{m/min}$.
2. Time $=\frac{288}{12}=24$ minutes.

Trick: Chase problems: time $=\frac{\text{gap}}{\text{speed difference}}$.

Answer: (A) 24 minutes

Concept: Total $=$ average $\times$ count; split the total in the given ratio.

1. Total age $=25\times 3=75$ years.
2. Ratio parts $=3+5+7=15$, one part $=5$.
3. Youngest $=3\times 5=15$ years.

Trick: Middle term of an evenly spaced ratio (5 parts) equals the average: $5x=25$, so $x=5$.

Answer: (D) 15 years

Concept: If numbers are in ratio $a:b$ (co-prime) with HCF $h$, the numbers are $ah$ and $bh$.

1. $12\times 25=300$.
2. $7\times 25=175$.

Trick: Check: $300:175=12:7$ and HCF$(300,175)=25$.

Answer: (B) 300, 175

Concept: Profit $\%=\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100$ for the quantity actually given.

1. Let CP of 1000 g $=$ ₹100; he charges $90$ (10% loss) but gives only 750 g.
2. CP of 750 g $=$ ₹75.
3. Profit $\%=\frac{90-75}{75}\times 100=20\%$.

Trick: $\frac{100-\text{loss}\%}{100-\text{less weight}\%}=\frac{90}{75}=1.2$, i.e. $20\%$ profit.

Answer: (B) 20%

Concept: Wages are shared in the ratio of work done.

1. A works $5+5=10$ days in all; A\'s work $=\frac{10}{25}=\frac{2}{5}$.
2. B did the remaining $\frac{3}{5}$.
3. A\'s share $=\frac{2}{5}\times 36000=14400$.

Trick: B\'s efficiency is not needed – A\'s total days alone decide his fraction.

Answer: (A) ₹14,400

Concept: Missing value $=$ required total $-$ sum of known values.

1. Required total $=6050\times 5=30250$.
2. Known sum $=5445+5937+5865+6562=23809$.
3. Fifth day $=30250-23809=6441$.

Trick: Deviation method: $-605-113-185+512=-391$, so fifth $=6050+391=6441$.

Answer: (C) ₹6,441

Concept: Male employees $=$ total $-$ female.

1. P: $4560-2210=2350$.
2. R: $3052-1280=1772$.
3. Difference $=2350-1772=578$.

Trick: Compute only the two rows asked.

Answer: (B) 578

Concept: Males $=\frac{\text{male part}}{\text{sum of parts}}\times \text{population}$.

1. Chennai ratio $11:9$, total parts $=20$.
2. Males $=\frac{11}{20}\times 200000=110000$.

Trick: One part $=200000÷20=10000$; males $=11$ parts.

Answer: (A) 1,10,000

Concept: Find the value of one ratio part from the given difference.

1. Glass $-$ wood $=5-3=2$ parts $=144$, so 1 part $=72$.
2. Plastic $=2\times 72=144$.
3. After $25\%$ increase: $144\times 1.25=180$.

Trick: 144 is the old number of plastic boxes – a trap option.

Answer: (D) 180

Concept: $x\%=\frac{x}{100}$.

1. $\frac{1}{5}\%=\frac{1}{5}\times \frac{1}{100}$.
2. $=\frac{1}{500}$.

Trick: $1\%=\frac{1}{100}$, so a fifth of it is $\frac{1}{500}$.

Answer: (D) $\frac{1}{500}$