Q&A: practice questions with answers

Concept: For successive discounts, multiply the marked price by $(1-\frac{d_1}{100})(1-\frac{d_2}{100})$.

1. After 10%: $18000\times 0.9=16200$
2. After 5%: $16200\times 0.95=15390$
3. SP = ₹15,390

Trick: Net discount $=10+5-\frac{10\times 5}{100}=14.5\%$; $18000\times 0.855=15390$.

Answer: (D) ₹15,390

Concept: $\sqrt{0.0256}=\frac{\sqrt{256}}{100}$ – halve the number of decimal places.

1. $\sqrt{256}=16$
2. $\sqrt{0.0256}=0.16$ and $\sqrt{4.41}=2.1$
3. $16+0.16-2.1=14.06$

Trick: Decimal places in root = half of those in the number (4 → 2, 2 → 1).

Answer: (A) 14.06

Concept: $14=2\times 7$, so the number must be even and divisible by 7.

1. 6436639 is odd – rejected.
2. $7048048$: split as $7048|048$; $7048-48=7000$, which is divisible by 7 (also $7048048=7\times 1006864$).
3. 6794266 and 7132968 leave non-zero remainders on division by 7.

Trick: Pattern abcabc… like 7048|048: 1001 = 7 × 11 × 13 helps – check $7048-048$.

Answer: (C) 7048048

Concept: For the same time period, profit is shared in the ratio of investments.

1. Salman's share $=16000-6400=9600$; ratio $S:V=9600:6400=3:2$
2. Total $45200=5$ parts, so 1 part $=\frac{45200}{5}=9040$
3. Difference $=3-2=1$ part $=9040$

Trick: Difference of investments = $\frac{\text{difference of shares}}{\text{total profit}}\times 45200=\frac{3200}{16000}\times 45200$.

Answer: (C) ₹9,040

Concept: If interests are equal for the same time, sums are in the inverse ratio of rates: $P_1\times R_1=P_2\times R_2$.

1. $P_1:P_2=11:14$ (sum at 14% : sum at 11%)
2. Total parts $=25$, so 1 part $=\frac{20400}{25}=816$
3. Sum at 14% $=11\times 816=8976$

Trick: Time (9 years) cancels – it is not needed at all.

Answer: (A) 8,976

Concept: $a^m÷a^n=a^{m-n}$ and $a^m\times a^n=a^{m+n}$; work left to right.

1. ${26}^{-19}÷{26}^{18}={26}^{-19-18}={26}^{-37}$
2. ${26}^{-37}\times {26}^3={26}^{-37+3}={26}^{-34}$

Trick: Just add/subtract powers: $-19-18+3=-34$.

Answer: (C) ${26}^{-34}$

Concept: Surface area of a sphere $=4\pi r^2$.

1. Diameter $=14\text{cm}$, so $r=7\text{cm}$
2. $S=4\pi \times 7^2=4\times 49\pi =196\pi {\text{cm}}^2$

Trick: In terms of diameter: $S=\pi d^2=\pi \times {14}^2=196\pi$.

Answer: (D) $196\pi {\text{cm}}^2$

Concept: Find both values separately and subtract.

1. $65\%\text{ of }75=\frac{65\times 75}{100}=48.75$
2. $\frac{2}{5}\text{ of }55=22$
3. Difference $=48.75-22=26.75$

Trick: $65\%$ of 75 = 75% of 65 = $\frac{3}{4}\times 65=48.75$.

Answer: (B) 26.75

Concept: Angle sum of a triangle is ${180}^{\circ }$; an exterior/linear pair adds to ${180}^{\circ }$.

1. In right $△BDC$: $\angle C={180}^{\circ }-{90}^{\circ }-{25}^{\circ }={65}^{\circ }$
2. In $△AEC$: $\angle AEC={180}^{\circ }-{80}^{\circ }-{65}^{\circ }={35}^{\circ }$
3. $\angle AEB={180}^{\circ }-{35}^{\circ }={145}^{\circ }$ (linear pair on BC)

Trick: $\angle AEB$ is exterior to $△AEC$: $\angle AEB=\angle CAE+\angle C={80}^{\circ }+{65}^{\circ }={145}^{\circ }$.

Answer: (D) ${145}^{\circ }$

Concept: If $n(n+1)=812$, then $n\approx \sqrt{812}$.

1. $\sqrt{812}\approx 28.5$, so try $28\times 29$
2. $28\times 29=812$ ✓
3. Greater number $=29$

Trick: Unit digit 2 → pairs ending (3,4), (8,9) etc.; near $\sqrt{812}$ → 28 and 29.

Answer: (A) 29

Concept: Profit = Selling price of the goods actually sold − Total cost price.

1. Total CP $=93$ bulbs for ₹93, so CP $=₹93$.
2. Bulbs left $=93-19=74$.
3. SP $=74\times 1.40=₹103.60$.
4. Profit $=103.60-93=₹10.60$.

Trick: Broken items add to cost but give no revenue — always count only the remaining items for SP.

Answer: (B) ₹10.60

Concept: For two numbers, $\text{HCF}\times \text{LCM}=\text{First number}\times \text{Second number}$.

1. $6\times 264=66\times x$
2. $x=\frac{6\times 264}{66}=\frac{1584}{66}=24$
3. Check: HCF$(66,24)=6$ ✓

Trick: $264÷66=4$, so other number $=6\times 4=24$ instantly.

Answer: (D) 24

Concept: $\text{SI}=\frac{P\times R\times T}{100}$ and Amount $=P+\text{SI}$.

1. $8\frac{4}{7}=\frac{60}{7}$ years. $7344=\frac{P\times 6.8\times 60}{700}$
2. $P=\frac{7344\times 700}{408}=18\times 700=₹12600$
3. New SI $=\frac{12600\times 9.7}{100}\times \frac{20}{3}=126\times 9.7\times \frac{20}{3}=₹8148$
4. Amount $=12600+8148=₹20748$

Trick: $7344÷408=18$ — spot this to get $P$ quickly.

Answer: (C) ₹20,748

Concept: Simplify the inner bracket first, then take LCM of denominators.

1. $1+\frac{3}{8}=\frac{11}{8}$, so $\frac{1}{11/8}=\frac{8}{11}$
2. Expression $=\frac{5}{2}+\frac{8}{11}-\frac{3}{5}$
3. LCM of 2, 11, 5 $=110$: $\frac{275+80-66}{110}=\frac{289}{110}$

Trick: Value $\approx 2.5+0.73-0.6=2.63$; only $\frac{289}{110}\approx 2.63$ fits.

Answer: (B) $\frac{289}{110}$

Concept: Distance is fixed, so $\text{Speed}\times \text{Time}$ is constant.

1. Distance $=48\times 9=432\text{km}$
2. Required speed $=\frac{432}{12}=36\text{km/h}$

Trick: $S_1{T}_1=S_2{T}_2$: $48\times \frac{9}{12}=36$.

Answer: (C) 36 km/hr

Concept: Convert both statements into linear equations in $M$ (Mary) and $D$ (Dia) and solve.

1. $2M=5D+27$
2. $7D=M-9\Rightarrow M=7D+9$
3. $2(7D+9)=5D+27\Rightarrow 9D=9\Rightarrow D=1$
4. $M=16$; difference $=16-1=15$ years

Trick: Substitute $M$ from the simpler equation into the other one.

Answer: (B) 15

Concept: $\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}$ (not the average of speeds).

1. Times: $\frac{294}{42}=7$, $\frac{210}{30}=7$, $\frac{330}{66}=5$ hours
2. Total time $=19$ h; total distance $=294+210+330=834\text{km}$
3. Average speed $=\frac{834}{19}=43.89\text{km/h}$

Yaad rakhein: Never take the simple mean $\frac{42+30+66}{3}=46$ — it is wrong when times differ.

Answer: (B) 43.89

Concept: When time is the same, profit is shared in the ratio of investments.

1. Ratio $=1370:1500:1230=137:150:123$
2. Sum of ratio $=410$
3. Simran's share $=\frac{123}{410}\times 1010=0.3\times 1010=₹303$

Trick: $\frac{123}{410}=\frac{3}{10}$ exactly — so Simran gets 30% of the profit.

Answer: (D) ₹303

Concept: Take CP $=100$ and follow mark-up and discount.

1. CP $=100\Rightarrow$ List price $=125$
2. SP $=125\times 0.84=105$, profit $=5$ units
3. 5 units $=₹140\Rightarrow$ 1 unit $=₹28$
4. List price $=125\times 28=₹3500$

Trick: Net effect $=25-16-\frac{25\times 16}{100}=+5\%$ profit.

Answer: (A) 3,500

Concept: $\text{SP}=\text{MP}\times (1-\frac{x}{100})\times (1-\frac{10}{100})$.

1. $39250\times 0.9=35325$
2. $1-\frac{x}{100}=\frac{32499}{35325}=0.92$
3. $x=8$

Trick: Check options: $39250\times 0.92\times 0.9=32499$ ✓.

Answer: (D) 8