Q&A: practice questions with answers

Concept: If one quantity is unchanged, keep its ratio term equal in both ratios.

1. Red 7 : Blue 5 → after removal 7 : 4 (red term already same)
2. Blue drops 5 → 4, i.e. 1 part = 12
3. Red = $7\times 12=84$

Trick: Red is a multiple of 7 – among options only 84 is ($84=7\times 12$).

Answer: (A) 84

Concept: $A=P{(1+\frac{R}{100})}^n$.

1. $A=12000\times (1.12{)}^3$
2. $(1.12{)}^3=1.2544\times 1.12=1.404928$
3. $A=12000\times 1.404928\approx 16859.13$ (₹)

Trick: Estimate: SI for 3 years = 4320 → amount just above 16,320; only ₹16,859 is near.

Answer: (B) ₹16,859.13

Concept: Adding the same amount keeps the difference unchanged.

1. 5 : 4 (difference 1) and 7 : 6 (difference 1) → parts match directly.
2. $5x+6000=7x\Rightarrow 2x=6000\Rightarrow x=3000$
3. Karan = $4\times 3000=12000$ (₹)

Trick: Difference same → $7-5=2$ parts = 6000.

Answer: (B) ₹12,000

Concept: Any number divisible by all = multiple of their LCM.

1. $15=3\times 5$, $20=2^2\times 5$, $25=5^2$
2. $\text{LCM}=2^2\times 3\times 5^2=300$
3. Among options, the smallest multiple of 300 is 1500.

Trick: 6400 and 12500 fail divisibility by 3 (digit sum); then pick the smaller of 1500 and 3000.

Answer: (A) 1500

Concept: For equal distances, average speed = $\frac{2xy}{x+y}$.

1. $=\frac{2\times 20\times 16}{20+16}$
2. $=\frac{640}{36}=17.78$ km/h ≈ 17.7

Trick: Average must lie between 16 and 20 – only 17.7 qualifies.

Answer: (C) $17.7\mathrm{km}/h$

Concept: If (divisor − remainder) is the same k for all, $\text{number}=\text{LCM}\times n-k$.

1. $8-3=12-7=20-15=5$
2. LCM(8, 12, 20) = 120
3. Smallest = $120-5=115$

Trick: Check: $115÷20$ leaves 15 ✓ – the other options fail this single test.

Answer: (B) 115

Concept: New average = old average + (net change in total ÷ count).

1. 40% of 15 = 6 numbers → +5 each = +30
2. 60% = 9 numbers → −3 each = −27
3. Net +3 → new average = $30+\frac{3}{15}=30.2$

Trick: Only net change matters: $0.4\times 5-0.6\times 3=2-1.8=+0.2$.

Answer: (C) 30.2

Concept: Moving towards each other, distances are in the ratio of speeds.

1. Speeds 65 : 45 = 13 : 9 (total 22)
2. Distance from M = $\frac{13}{22}\times 550$
3. $=13\times 25=325$ km

Trick: Time = $550÷110=5$ h → $65\times 5=325$.

Answer: (C) 325 km

Concept: Use total work = LCM and find individual daily rates.

1. Work = 140; $A+B=5$, $B+C=7$, $A+B+C=14$ per day
2. $C=14-5=9$, $A=14-7=7$ → $A+C=16$
3. Time = $140÷16=8.75=8\frac{3}{4}$ days

Trick: $A+C=2(A+B+C)-(A+B)-(B+C)=28-12=16$ units/day.

Answer: (B) $8\frac{3}{4}$ days

Concept: Work done together first; remaining work by the one who stays.

1. Work = 60; A = 3/day, B = 2/day
2. 3 days together = $3\times 5=15$ → left 45
3. B: $45÷2=22.5$ days

Trick: Together $\frac{1}{12}$ per day → 3 days = $\frac{1}{4}$ done; B does $\frac{3}{4}\times 30=22.5$.

Answer: (D) 22.5 days

Concept: $\text{Discount}\%=\frac{\text{MP}-\text{SP}}{\text{MP}}\times 100$.

1. Discount = $9000-7200=1800$ (₹)
2. $\%=\frac{1800}{9000}\times 100=20\%$

Trick: $\frac{\text{SP}}{\text{MP}}=\frac{7200}{9000}=0.8$ → 20% off.

Answer: (D) 20%

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

1. $R\times T=8\times 3=24\%$
2. $P=\frac{4800\times 100}{24}$
3. P = ₹20,000

Trick: 24% of P = 4800 → 1% = 200 → P = 20,000.

Answer: (D) ₹20,000

Concept: Difference of amounts = SI for the difference of years.

1. SI for 2 years = $3500-3000=500$ → 250/year
2. $P=3000-3\times 250=2250$
3. $R=\frac{250}{2250}\times 100=\frac{100}{9}=11\frac{1}{9}\%$

Trick: $\frac{250}{2250}=\frac{1}{9}$ → $\frac{1}{9}=11.11\%$.

Answer: (B) $11\frac{1}{9}\%$

Concept: Removed mixture carries both liquids in the same ratio.

1. Milk 30 L, water 20 L
2. Remove 10 L (6 milk, 4 water) → 24 : 16
3. Add 10 L water → 24 : 26 = 12 : 13

Trick: Milk = $30\times \frac{40}{50}=24$ directly; water = $50-24=26$.

Answer: (B) 12 : 13

Concept: ${\text{Tangent}}^2=\text{external part}\times \text{whole secant}$: $A{B}^2=AC\times AD$.

1. ${12}^2=8\times AD\Rightarrow 144=8AD$
2. AD = 18 cm
3. $y=CD=18-8=10$ cm

Trick: $8(8+y)=144\Rightarrow 8+y=18\Rightarrow y=10$.

Answer: (A) 10 cm

Concept: Price/market control in the Delhi Sultanate is linked with Alauddin Khalji.

1. Alauddin Khalji (1296–1316) fixed prices of grain, cloth, horses etc. to maintain a large army on low cash salaries.
2. Officers like the Shahna-i-Mandi supervised markets; hoarding and short-weighing were punished.
3. Balban – 'blood and iron'; Iltutmish – iqta and silver tanka; Muhammad bin Tughlaq – token currency.

Yaad rakhein: Alauddin also introduced the Dagh (branding horses) and Chehra (descriptive roll of soldiers) systems.

Answer: (C) Alauddin Khalji

Concept: The Indian Constitution borrowed several features from foreign constitutions.

1. From Canada: advisory jurisdiction of the Supreme Court (Art. 143), federation with a strong Centre, residuary powers with the Centre, Governor appointed by the Centre.
2. Rule of law – Britain; Fundamental Duties – USSR.
3. Federal structure as such is drawn mainly from the Government of India Act, 1935.

Yaad rakhein: Art. 143 – the President may seek the Supreme Court's opinion; the advice is not binding.

Answer: (C) Advisory jurisdiction of the Supreme Court

Concept: Article 25 guarantees freedom of conscience and the right to profess, practise and propagate religion.

1. 'Propagate' means spreading one's faith, not converting others.
2. Supreme Court (Rev. Stainislaus case, 1977): there is no fundamental right to convert another person.
3. So 'right to religious conversion' is not part of Article 25.

Yaad rakhein: Articles 25–28 = Right to Freedom of Religion; Art. 26 covers managing religious affairs/institutions.

Answer: (C) Right to religious conversion

Concept: AIIB is a China-led multilateral development bank.

1. Headquarters: Beijing, China; operational since January 2016.
2. India is a founding member and the second-largest shareholder after China.

Yaad rakhein: Asian Development Bank (ADB) HQ – Manila; New Development Bank (BRICS) HQ – Shanghai.

Answer: (A) Beijing

Concept: India and Japan signed a civil nuclear cooperation pact during PM Modi's 2016 Tokyo visit.

1. Signed on 11 November 2016; came into force in July 2017.
2. It was Japan's first such deal with a country outside the NPT.

Yaad rakhein: India–US civil nuclear deal (123 Agreement) was finalised in 2008.

Answer: (C) 2016