Q&A: practice questions with answers

Concept: Use standard fraction values of common percentages.

1. $12\frac{1}{2}\%=\frac{1}{8}\to \frac{480}{8}=60$ km.
2. $66\frac{2}{3}\%=\frac{2}{3}\to 270\times \frac{2}{3}=180$ km.
3. Total = $60+180=240$ km.

Trick: Learn: $12\frac{1}{2}\%=\frac{1}{8}$, $16\frac{2}{3}\%=\frac{1}{6}$, $33\frac{1}{3}\%=\frac{1}{3}$, $66\frac{2}{3}\%=\frac{2}{3}$, $87\frac{1}{2}\%=\frac{7}{8}$.

Answer: (A) 240 km

Concept: Commission = rate % × selling price, then scale by quantity and days.

1. Shirt: 2% of 600 = ₹12; tie: 12% of 150 = ₹18.
2. Per day: $3\times 12+4\times 18=36+72=$ ₹108.
3. 60 days: $108\times 60=$ ₹6,480.

Trick: Answer must be a multiple of 60 and of 108 → $6480÷108=60$ ✓.

Answer: (C) ₹6480

Concept: $\text{Real profit factor}=(\text{price factor})÷(\text{weight actually given})$.

1. He gets 90% of CP for the amount he claims to sell.
2. He gives only 75% of that weight.
3. Factor = $\frac{0.90}{0.75}=1.2$ → 20% profit.

Trick: Short-cut: $\frac{100-\text{loss}}{100-\text{weight cut}}=\frac{90}{75}=\frac{6}{5}$ → 20% gain.

Answer: (C) 20%

Concept: If profit at $S{P}_1$ equals loss at $S{P}_2$, then $CP=\frac{S{P}_1+S{P}_2}{2}$.

1. $CP=\frac{2200+1800}{2}=$ ₹2000.
2. At ₹2150: profit = ₹150.
3. Profit% = $\frac{150}{2000}\times 100=7.5\%$.

Trick: ₹2150 > CP, so it is a profit – options B and D drop out immediately.

Answer: (C) Profit of 7.5%

Concept: Express the new selling price in terms of CP.

1. $P=1.3CP$.
2. Offer price after 10% off = $1.5P\times 0.9=1.35P=1.35\times 1.3CP=1.755CP$.
3. Profit = 75.5%.

Trick: Multiply factors directly: $1.3\times 1.5\times 0.9=1.755$ → profit 75.5%.

Answer: (C) 75.5%

Concept: Net % = markup − discount − $\frac{\text{markup}\times \text{discount}}{100}$.

1. Take CP = 100 → MP = 120.
2. SP = $120\times 0.9=108$.
3. Profit = 8%.

Trick: $20-10-\frac{20\times 10}{100}=8\%$.

Answer: (B) 8%

Concept: Write SP in two ways – via MP and via required profit – and equate.

1. Let $CP=x$; $MP=1.5x$; after 20% off $=1.2x$.
2. After ₹300 cash discount: $1.2x-300$.
3. This equals $1.14x\to 0.06x=300\to x=$ ₹5000.

Trick: Gap between 20% and 14% profit = 6% of CP = ₹300 → $CP=\frac{300\times 100}{6}=5000$.

Answer: (B) ₹5000

Concept: Find the mixture's cost price first, then use alligation.

1. CP of mixture = $43.70÷1.15=$ ₹38/kg.
2. Alligation: cheaper (₹32) : dearer (₹45) = $(45-38):(38-32)=7:6$.
3. Dearer = $24\times \frac{6}{7}=20.57\approx 20.5$ kg.

Trick: $\frac{43.70}{1.15}$: since $1.15\times 38=43.70$, mixture CP = 38 directly.

Answer: (C) 20.5 kg

Concept: Slant height $l=\sqrt{r^2+h^2}$.

1. $r=\frac{14}{2}=7$ cm, $h=24$ cm.
2. $l^2=49+576=625\to l=25$ cm.

Trick: 7, 24, 25 is a Pythagorean triplet.

Answer: (A) 25 cm

Concept: $SI=\frac{P\times R\times T}{100}$; add both interests and solve for R.

1. Sudhir: $\frac{5000\times 2\times R}{100}=100R$.
2. Vinod: $\frac{3000\times 4\times R}{100}=120R$.
3. $220R=4400\to R=20\%$.

Trick: Total 'principal-years' = $10,000+12,000=22,000$; $\frac{4400}{22,000}=20\%$.

Answer: (D) 20%

Concept: Volume of a prism = base area × height.

1. New height = $16\times 1.25=20$ cm.
2. Volume = $25\times 20=500$ cm³.

Trick: Old volume 400 cm³; +25% → 500 cm³.

Answer: (C) 500 cm³

Concept: Area varies as $r^2$, so use the successive change formula.

1. New area factor = ${0.8}^2=0.64$.
2. Decrease = $1-0.64=0.36$ → 36%.

Trick: $-20-20+\frac{20\times 20}{100}=-36\%$.

Answer: (C) 36%

Concept: For equal perimeter, find each area and compare.

1. Circle: $r=\frac{160}{2\pi }=\frac{80}{\pi }$ → area = $\frac{6400}{\pi }\approx 2037$ m².
2. Square: each side $\frac{160}{4}=40$ m, so its area is ${40}^2=1600$ m².
3. Ratio = $\frac{6400}{1600\pi }=\frac{4}{\pi }\approx 1.27$.

Trick: For any equal perimeter, circle : square area = $4:\pi \approx 1.27:1$.

Answer: (B) 1.27 : 1

Concept: Volume of the immersed solid = volume of liquid raised.

1. Hemisphere volume = $\frac{2}{3}\pi \times 6^3=144\pi$ cm³.
2. Raised oil: $2.5\times \pi R^2=144\pi$, so $R^2=\frac{144}{2.5}=57.6$.
3. Taking the square root, $R\approx 7.59$ cm.

Trick: ${7.5}^2=56.25$ and ${7.6}^2=57.76$, so R is just under 7.6 – only 7.59 fits.

Answer: (B) 7.59 cm

Concept: In the same circle, sector area depends only on the central angle.

1. $\frac{3\pi }{4}\text{rad}=\frac{3}{4}\times {180}^{\circ }={135}^{\circ }$.
2. Both angles are 135° with the same radius.
3. Areas are equal → ratio 1 : 1.

Trick: Convert radians to degrees with $\times \frac{180}{\pi }$ before comparing.

Answer: (C) 1 : 1

Concept: A synonym has the same meaning as the given word.

1. Vague = not clearly expressed or defined; hazy.
2. Nebulous = unclear, cloud-like, ill-defined → same sense.
3. Precise and Obvious are opposites; Stable is unrelated.

Trick: Nebula = cloud → 'nebulous' = cloudy/unclear, like 'vague'.

Answer: (C) Nebulous

Concept: Erudite = deeply learned; the blank needs its opposite.

1. 'Very little formal education' signals lack of knowledge.
2. Uninformed = lacking knowledge → opposite of erudite.
3. Intellectual, Educated, Scholarly all mean the same as erudite.

Trick: When three options are synonyms of each other, the odd one is usually the antonym.

Answer: (B) Uninformed

Concept: 'Fly off the handle' = to lose one's temper suddenly.

1. The image is of an axe-head flying loose from its handle – sudden and out of control.
2. The manager became suddenly furious on seeing serious errors.

Yaad rakhein: Similar idioms: blow one's top, hit the roof, see red – all mean sudden anger.

Answer: (A) React with sudden and uncontrolled anger

Concept: Panegyric = a speech or text of high public praise.

1. Homage, Encomium and Praise all express honour/praise – synonyms.
2. Castigation = severe criticism or punishment → opposite.

Trick: Three praise words cancel each other out; the only negative word is the antonym.

Answer: (D) Castigation

Concept: Check each word letter by letter against the standard spelling.

1. Trisomy (an extra chromosome, e.g. Down syndrome) has a single 's'.
2. 'Trissomy' adds an extra s → wrong.
3. Trinket, Trisomic, Trifold are correct.

Trick: Trisomic (given as correct) shows the root 'tri-som' – so trisomy must also have one s.

Answer: (B) Trissomy