CAT 50 Day Streak Day 32

Day 32 / 50

CAT 50 Day Streak – Day 32

30 questions across VARC, DILR & QA · +3 for a correct answer · −1 for a wrong MCQ · no negative marking for TITA

0/30Attempted
0Correct
0Wrong
0Score / 90

VARC · Verbal Ability & Reading Comprehension

Q1 – Q10 0/10
Passage · Q1 – Q4

There are various reasons why collapse could benefit human welfare. States often demanded tax in the form of grain. Without tax collectors passing by, people often had more to eat. More than that, without the pressure to grow tax crops, they often diversified their diet to include more animal protein, which beget stronger bones. A flight away from cities towards rural areas also meant less circulation of infectious disease. Finally, a more complex reason in at least some cases is a survivor effect. Some collapses did lead to population declines: sometimes death (which was obviously bad for those citizens) but, as we’ll see later, also because people moved.

Either way, this meant that workers sticking around became scarcer and more valuable labour: they could bargain with their employers for better wages. Which is why we see both heights and wages rise after the Black Death in the 14th century. Women’s heights appear to have decreased, but this is likely due to an earlier onset of menarche (the first menstrual cycle, which slows growth). Earlier menarche often occurs when girls experience better living conditions with more resources, counterintuitively resulting in lower long-term height. Hence the decreasing height of women is likely an indicator that they too were benefitting after the Black Death.

Perhaps the most neglected reason for post-collapse health boosts is that most states of the past were predatory, fuelling enormous inequality and impoverishing the masses. One review of 28 premodern states, from the time of Rome to 1947, found that they were on average more than three-quarters towards the theoretical maximum level of wealth inequality. That maximum is a situation in which one person owns all the surplus resources while everyone else is left with meagre subsistence (just enough to survive and reproduce). The most reliable effect of collapse was to level these wealth inequalities.

All this helps to explain why the adoption of agriculture and states were an enormous blow to human health. Not only did human height shrink but bones got weaker, teeth filled with more holes, and new infectious diseases such as influenza and the plague began as people were crammed together with animals. Men today are on average still shorter than their ancestors during the stateless ice age (or at least the male skeletons we’ve found in Europe; evidence elsewhere is sparse, but we have little reason to think that Europeans were especially tall).

Improved welfare after a state breaks down is not a purely ancient phenomenon either. That is clear when we look at the case of the collapse of Somalia in 1991. The Barre regime that had previously ruled the country fell apart; local warlords and traditional groups took the reins of governance. While there was increased conflict, it was not a nightmare for human wellbeing. Instead, almost every quality-of-life indicator in the country, from infant mortality to extreme poverty, improved. This wasn’t just Somalia experiencing a region-wide improvement due to better technology and aid. Its improvements significantly outstripped those of its intact, stable neighbours.

Q1MCQ
The author mentions the decrease in women's heights after the Black Death primarily to:
Astrengthen the argument for improved welfare by pre-empting and resolving an apparent contradiction.
Bargue that the benefits of the survivor effect were not shared equally between men and women.
Cintroduce a paradox that is left unresolved, suggesting the data is inconclusive.
Dsuggest that the survivor effect led to nutritional deficiencies for women but not for men.
Solution Answer: A

Falling heights for women would seem to contradict the claim that welfare improved. The author heads off that objection by explaining it as earlier menarche, which comes from better living conditions. The conclusion is that women “too were benefitting”.

B and D are the opposite: the author says women benefitted as well. C: the paradox is explicitly resolved, not left open.

Q2MCQ
The author discusses the case of Somalia in 1991 for all of the following reasons EXCEPT:
Ato show that a breakdown in a formal state structure does not invariably lead to a nightmare for human well-being.
Bto counter the potential argument that the benefits of collapse are a purely ancient phenomenon.
Cto demonstrate that the quality-of-life improvements were not simply part of a wider, regional trend.
Dto argue that governance by local warlords is superior to governance by a centralized regime.
Solution Answer: D

The author only reports that quality-of-life indicators improved after the collapse, and even notes “increased conflict”. Nowhere does the author claim warlord rule is a superior form of government.

A matches “it was not a nightmare for human wellbeing”. B matches “not a purely ancient phenomenon either”. C matches the point that Somalia’s gains outstripped those of its stable neighbours.

Q3MCQ
Which of the following scenarios best exemplifies the theoretical maximum level of wealth inequality described in paragraph 3?
AA society where the top 1% controls 90% of all wealth, while the bottom 99% controls the remaining 10%.
BA society where all resources are owned by a single entity, which provides the rest of the population with just enough food and shelter to survive and reproduce.
CA society where a ruling class demands high grain taxes, forcing farmers to abandon more nutritious crops.
DA society where scarce labor after a plague allows workers to successfully bargain for higher wages and better working conditions.
Solution Answer: B

The maximum is defined as “one person owns all the surplus resources while everyone else is left with meagre subsistence (just enough to survive and reproduce)”. B mirrors this exactly.

A is extreme inequality but not the maximum, since the 99% still hold 10%. C describes predatory taxation, not the inequality limit. D describes the levelling that follows a collapse.

Q4MCQ
Which of the following, if true, would most seriously weaken the author's argument?
ANew evidence from Asia shows that premodern states there were significantly less unequal than those in Europe.
BThe survivor effect is shown to be a rare phenomenon, as most population declines are quickly offset by high birth rates.
CA study of 20th-century state collapses finds that 19 out of 20 led to immediate and catastrophic famines and disease outbreaks.
DIt is discovered that the stateless ice-age skeletons found in Europe were from a genetically distinct and taller subspecies of human.
Solution Answer: C

The core claim is that collapse can improve human welfare, and Somalia is offered as modern proof. If almost all modern collapses caused famine and disease, Somalia becomes an outlier and the central claim collapses.

A: the review covered states from Rome onward, and Asian states being less unequal doesn’t remove the other benefits. B removes only one of several reasons the author gives. D undercuts only the ice-age height comparison, a side point.

Q5TITA
The four sentences (labelled 1, 2, 3 and 4) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer.
  1. When AI systems lack adequate exposure to a language, they have blind spots in their comprehension of human experience.
  2. What’s even more concerning is the imbalance between how many people speak a language in the physical world and how much that language is represented in online data.
  3. For example, data from Common Crawl, one of the largest public sources of training data, reveals stark inequalities.
  4. It contains more than 300 billion web pages spanning 18 years, but English dominates with 44 per cent of the content.
Solution Answer: 1342

The order runs like this:

  • 1: The general claim: too little exposure to a language creates blind spots in AI.
  • 3: “For example”, Common Crawl data shows stark inequalities.
  • 4: “It” (Common Crawl) has 300 billion pages, 44% of them in English.
  • 2: “What’s even more concerning” escalates to the mismatch between speakers and online presence.
Q6MCQ
There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence If the richest people and nations voluntarily cut their carbon footprint, the entire world would benefit.
Paragraph Tackling climate change is an inherently collectivist endeavour. ___(1)___. We only have one planet, with one atmosphere, and whenever anyone in the world emits greenhouse gases, we all feel the effects. ___(2)___. But some people have an outsized influence. Globally, the wealthiest 1 per cent are responsible for one-fifth of all emissions since 1990. ___(3)___. What if the wealthiest instead try to fix their carbon imbalance by funding geoengineering efforts that aim to cool the planet back down? ___(4)___. Here, the promise of global benefit is less certain.
AOption 1
BOption 2
COption 3
DOption 4
Solution Answer: C (Option 3)

Blank 3 comes right after the statistic on the wealthiest 1 per cent, so the sentence follows naturally: if the richest cut their footprint, everyone benefits. The next sentence asks what happens if they “instead” fund geoengineering, which needs this first option to contrast with. “Here, the promise of global benefit is less certain” then echoes “the entire world would benefit”.

At blanks 1 and 2 the richest haven’t been introduced yet. At blank 4 the sentence would separate the geoengineering question from its answer.

Q7TITA
Five jumbled-up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
  1. The question is easier to grasp by looking at fields in which formal systems have long played a central role.
  2. There is no single physical theory that explains everything.
  3. Physics, for instance, has relied on formalisation for centuries.
  4. But what, exactly, does it mean to formalise something like ethics?
  5. Still, many have tried to formalise ethics by treating certain moral claims not as conclusions but as starting points.
Solution Answer: 5

The coherent paragraph is 4 → 1 → 3 → 2:

  • 4: The question: what does it mean to formalise ethics?
  • 1: “The question” is easier to grasp by looking at fields built on formal systems.
  • 3: “Physics, for instance”, has relied on formalisation for centuries.
  • 2: Even so, no single physical theory explains everything.

Sentence 5 jumps to a specific method people have used to formalise ethics. The paragraph is still clarifying what formalisation means through the physics analogy, and “Still” has no claim about ethics to push against.

Q8MCQ
The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Passage Drug addiction, immigration violations, and mental illness are rampant among the homeless population, so it's cruel to deny funds to groups that are on the front lines of the problem. Gender issues shouldn't even come into play here. These groups need to assist anyone in dire straits. The feds ought to focus on providing help, not advance their tangential cultural agendas. Nevertheless, I agree with the administration's expectation that funding recipients "operate in a city, county, or state that prohibits public camping." Unlike those other rules, this one applies directly to the homelessness problem. The U.S. Supreme Court's Grant's Pass decision last year finally freed localities to clear out park encampments. It overturned the Ninth Circuit's wacky Boise decision, which considered anti-camping statutes to be cruel and unusual punishment. Many California cities have taken advantage of the new latitude. Those that don't should look for funding elsewhere.
AThe author believes homelessness is caused mainly by addiction and mental illness, and therefore, federal funding should only go to rehabilitation programs.
BThe author criticizes the government for prioritizing cultural issues over practical measures to combat homelessness and supports restricting funds to cities that prohibit public camping.
CThe author supports all of the administration’s homelessness policies, particularly those allowing cities to remove encampments from public spaces.
DThe author argues that homelessness policy should focus on compassion and inclusivity rather than legal restrictions or ideological concerns.
Solution Answer: B

The author has two points. The feds should stop pushing “tangential cultural agendas” and focus on help, but the anti-camping condition is right because it bears directly on homelessness. B captures both.

A: addiction and mental illness are described as rampant, not as the main cause, and nothing limits funding to rehabilitation. C: the author rejects some rules (the gender conditions), so it is not “all”. D: the author explicitly supports a legal restriction on camping.

Q9TITA
Five jumbled-up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.
  1. In 2013, together with his student Gerald Carter, Wilkinson set out to gauge the relative importance of friendship, based on the reciprocal exchange of meals versus that based on genetic kinship, in driving blood sharing.
  2. Over the years, and then the decades, a much clearer picture of friendship among vampire bats has emerged.
  3. So, blood sharing is more powerful than gene sharing.
  4. After testing the waters, as Wilkinson and his colleagues describe it, the bats then took friendship to the next level and began the exchange of blood meals.
  5. Friendship was 8.5 times more important!
Solution Answer: 4

The coherent paragraph is 2 → 1 → 5 → 3:

  • 2: Over decades, a clearer picture of vampire-bat friendship emerged.
  • 1: In 2013, Wilkinson and Carter compared friendship with kinship as drivers of blood sharing.
  • 5: The result: friendship was 8.5 times more important.
  • 3: “So”, blood sharing beats gene sharing.

Sentence 4 describes how bat friendships develop step by step (“testing the waters”). That is a different point from the friendship-versus-kinship study, and it would break the study → result → conclusion chain.

Q10TITA
The four sentences (labelled 1, 2, 3 and 4) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer.
  1. To avoid that unsettling implication, he introduced a variable, Λ, the Greek symbol for lambda, to balance his equation.
  2. According to his math, the universe should be volatile over time, either expanding or contracting.
  3. In November 1915, he presented the equations underlying his general theory of relativity; 15 months later, he applied those equations to, as he phrased the topic in the paper’s title, “cosmological considerations.”
  4. Albert Einstein, the second theorist who paved the way for the expansion discovery, did conceive of it.
Solution Answer: 4321

The order runs like this:

  • 4: It introduces Einstein by full name.
  • 3: “He” presented general relativity, then applied it to cosmology.
  • 2: “According to his math”, the universe should expand or contract.
  • 1: “To avoid that unsettling implication”, he added lambda.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10
Set 1 · Q11 – Q16

The table below gives the marks of four students, Paul, Quinton, Ross and Sam, in three sections, namely VARC, DILR and QA. The list is sorted in ascending order of marks.

VARCDILRQA
41216
101620
122024
142428
  • Paul got distinct marks in the three sections.
  • Aggregate marks of Quinton and Sam are 58 and 52, respectively.
  • Ross got equal marks in two sections, and his aggregate score is more than that of Paul.
  • Quinton did not score 20 or 10 marks in any of the sections.
Q11TITA
For how many persons can we uniquely determine their marks in all sections?
Solution Answer: 1
  • Totals. All marks add up to 40 + 72 + 88 = 200. Quinton + Sam = 110, so Paul + Ross = 90, and since Ross > Paul, Ross > 45.
  • Quinton (58, no 10 or 20). VARC ∈ {4, 12, 14}, DILR ∈ {12, 16, 24}, QA ∈ {16, 24, 28}. The only combination summing to 58 is 14 + 16 + 28.
  • Sam (52). From what’s left (VARC 4/10/12, DILR 12/20/24, QA 16/20/24): (4, 24, 24), (12, 20, 20) or (12, 24, 16).
  • Ross and Paul. Ross needs two equal marks (12–12, 20–20 or 24–24), Paul needs three distinct marks, and Ross must outscore Paul. Testing each Sam option leaves four valid cases.
CasePaul (V/D/Q)Ross (V/D/Q)Sam (V/D/Q)Quinton (V/D/Q)
110/12/16 = 3812/20/20 = 524/24/24 = 5214/16/28 = 58
210/12/16 = 384/24/24 = 5212/20/20 = 5214/16/28 = 58
34/12/16 = 3210/24/24 = 5812/20/20 = 5214/16/28 = 58
44/12/24 = 4010/20/20 = 5012/24/16 = 5214/16/28 = 58

Only Quinton’s marks are the same in every case, so the answer is 1.

Q12MCQ
How many marks did Paul get in DILR?
A12
B16
C20
DCannot be determined
Solution Answer: A

From the table in Q11, Paul scores 12 in DILR in all four cases.

Q13TITA
What was the lowest score Quinton had in any of the sections?
Solution Answer: 14

From the table in Q11, Quinton scored 14, 16 and 28. His lowest is 14.

Q14MCQ
What is the maximum possible score of Ross?
A52
B54
C56
D58
Solution Answer: D

From the table in Q11, Ross scores 52, 52, 58 or 50. The maximum is 58 (case 3: 10/24/24).

Q15MCQ
What is the maximum possible score of Paul?
A38
B36
C40
D42
Solution Answer: C

From the table in Q11, Paul scores 38, 38, 32 or 40. The maximum is 40 (case 4: 4/12/24).

Q16MCQ
If all of them had a unique aggregate score, how many marks did Sam get in VARC?
A10
B12
C12 or 14
D10 or 14
Solution Answer: B

From the table in Q11: in cases 1 and 2, Ross = Sam = 52, and in case 3, Ross = Quinton = 58. Only case 4 gives four different totals (40, 50, 52, 58). There Sam scored 12 in VARC.

Set 2 · Q17 – Q20

Abhijeet, Deepak, Gitesh, Harsh, Narayan, Rishabh and Sanket play a popular video game. The game has player rating which is the average of ratings obtained in the matches played by the person. They played a tournament consisting of three games. The table below gives the ratings of these players in those games:

PlayerGame 1Game 2Game 3
Abhijeet805965
Deepak775670
Gitesh526785
Harsh626480
Narayan9177
Rishabh7671
Sanket7464

The rating is to be calculated in the following manner:

For instance, suppose Abhijeet had played 5 games before the start of the tournament and had a rating of 76, his rating after the tournament = {(76 × 5) + 80 + 59 + 65}/8 = 73

Q17MCQ
Gitesh had a rating of 79.4 and 77.5 before and after the tournament, respectively. How many games had he played before the tournament?
A10
B25
C15
D20
Solution Answer: C

Gitesh’s tournament total = 52 + 67 + 85 = 204. With n games before: 79.4n + 204 = 77.5(n + 3) = 77.5n + 232.5.

1.9n = 28.5, so n = 15.

Q18MCQ
Before the tournament, Deepak had played twice as the matches played by Harsh. After the tournament, Deepak’s rating dropped by 0.5 while that of Harsh dropped by 1. What was the difference between their ratings at the beginning of the tournament?
A1.5
B2.5
C3
DCannot be determined
Solution Answer: A

Let Harsh have played m games, so Deepak played 2m. Tournament totals: Deepak 77 + 56 + 70 = 203, Harsh 62 + 64 + 80 = 206.

Deepak: 2m·d + 203 = (2m + 3)(d − 0.5), which gives 3d = 204.5 + m.

Harsh: m·h + 206 = (m + 3)(h − 1), which gives 3h = 209 + m.

Subtracting: 3(h − d) = 4.5, so the difference is 1.5, whatever m is.

Q19TITA
Rishabh had played 13 games before the tournament. If his rating after the tournament increased from 72 to 72.5, what was his rating in game 1?
Solution Answer: 77

Total after 16 games = 72.5 × 16 = 1160. Total before = 72 × 13 = 936. The tournament contributed 224.

Game 1 = 224 − 76 − 71 = 77.

Q20MCQ
After the tournament, Narayan and Sanket had completed 15 and 21 games, respectively. Both had the same rating in game 3. If Sanket’s rating after the tournament increased from 68.5 to 69, by how much did Narayan’s rating increase?
A2.6
B2.7
C2.8
DCannot be determined
Solution Answer: D

Sanket played 18 games before. His tournament total = 69 × 21 − 68.5 × 18 = 1449 − 1233 = 216, so game 3 = 216 − 74 − 64 = 78. Narayan also scored 78, so his tournament total = 91 + 77 + 78 = 246.

Narayan played 12 games before, at an unknown rating r. His increase = (12r + 246)/15 − r = (246 − 3r)/15, which depends on r. So it cannot be determined.

QA · Quantitative Ability

Q21 – Q30 0/10
Q21MCQ
In the given figure, ABCD is a rectangle with sides BC = AD = 30 units and AB = CD = 90 units. ∠AFD is 30°, and ∠BEC is 60°. Find the length of the median of the trapezium ABEF.
Rectangle ABCD with AB = 90 and AD = 30; F and E lie on DC, with angle AFD = 30° and angle BEC = 60°, forming trapezium ABEF
A90 − 10√3
B90 − 15√3
C90 − 20√3
D90 − 30√3
Solution Answer: C

In right triangle ADF: DF = AD/tan 30° = 30√3. In right triangle BCE: EC = BC/tan 60° = 30/√3 = 10√3.

FE = 90 − 30√3 − 10√3 = 90 − 40√3.

Median = (AB + FE)/2 = (90 + 90 − 40√3)/2 = 90 − 20√3.

Q22MCQ
Naresh bought some shirts for Rs. 600 per shirt, but received 20% more of the lot for free. He marked up the cost by 40% and gave a discount of 10%, but a bargainer bought the entire lot and received 1 shirt free after buying 7 shirts. Find the profit percentage from the entire transaction?
A31.6%
B32.3%
C33.2%
D34.5%
Solution Answer: B

Say he pays for 10 shirts: cost = 6000, and he receives 12 shirts.

Selling price per shirt = 600 × 1.4 × 0.9 = 756. The bargainer pays for 7 of every 8 shirts: revenue = 12 × 756 × 7/8 = 7938.

Profit % = 1938/6000 × 100 = 32.3%.

Q23TITA
If x and y are integers and log3 x + log3 y ≥ 14, find the least value of x + y.
Solution Answer: 4374

For the logs to be defined, x and y must be positive. log3 x + log3 y = log3(xy) ≥ 14, so xy ≥ 314.

By AM ≥ GM, x + y ≥ 2√(xy) ≥ 2 × 37 = 2 × 2187 = 4374.

Equality holds at x = y = 2187, which are integers, so the least value of x + y is 4374.

Q24MCQ
What is the sum of all prime numbers less than 100 of the form a2 + b2, where a and b are distinct positive integers?
A466
B473
C502
D515
Solution Answer: D

An odd prime is a sum of two squares exactly when it leaves remainder 1 on division by 4. (2 = 12 + 12 is excluded because a and b must be distinct.)

Such primes below 100: 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97. Their sum = 515.

Q25TITA
Find the area (in sq cm) of a trapezium whose parallel sides measure 14 cm and 35 cm, and the oblique sides measure 13 cm and 20 cm.
Solution Answer: 294

Draw a line through one end of the shorter side, parallel to an oblique side. This cuts off a triangle with sides 13, 20 and 35 − 14 = 21.

By Heron’s formula, s = 27 and area = √(27 × 14 × 7 × 6) = 126. Height = 2 × 126/21 = 12.

Trapezium area = ½ × (14 + 35) × 12 = 294 sq cm.

Q26MCQ
S alone can complete a piece of work in 30 days. The ratio of the efficiencies of P to Q is 5:4, and that of R to P is 3:5. The ratio of the efficiencies of Q to S is 2:3. P, Q, R, and S work together in pairs of two to complete the work. The sequence of work is as follows: P pairs with Q, R, and S, respectively, for one day each (in that order). Next, Q pairs with R and S for one day each, and finally, R pairs with S for one day. The same sequence is then repeated continuously until the work is completed. If they continue working in this pattern, on which day will the work be completed?
A18th
B19th
C20th
D21st
Solution Answer: D

Efficiencies: P = 5, Q = 4, R = 3, S = 6. Total work = 6 × 30 = 180 units.

One 6-day cycle: PQ 9, PR 8, PS 11, QR 7, QS 10, RS 9, for 54 units. Three cycles (18 days) complete 162 units, leaving 18.

Day 19 (PQ): 171. Day 20 (PR): 179. Day 21 (PS) finishes the work, so it is completed on the 21st day.

Q27MCQ
A club is having a lottery. There are two prizes to be won. Every member of the club submits exactly one entry, and these entries are stored in a box. After this is done, Praveen sneaks 6 extra entries with his name into the box. The chance of him winning both prizes is 7%. How many people are members of the club?
A25
B19
C44
D32
Solution Answer: B

With n members, the box holds n + 6 entries, and 7 of them are Praveen’s. Drawing two without replacement: (7/(n + 6)) × (6/(n + 5)) = 7/100.

(n + 6)(n + 5) = 600 = 25 × 24, so n + 5 = 24 and n = 19.

Q28MCQ
If p and q are roots of x2 + 7x + 12 = 0, then the equation whose roots are (p + q)2 and (p – q)2 is
Ax2 – 50x + 49 = 0
Bx2 + 50x – 49 = 0
Cx2 + 50x + 49 = 0
Dx2 – 50x – 49 = 0
Solution Answer: A

p + q = −7 and pq = 12. So (p + q)2 = 49, and (p − q)2 = 49 − 4 × 12 = 1.

The new roots are 49 and 1: sum 50, product 49. The equation is x2 − 50x + 49 = 0.

Q29TITA
Pushkin took his dog for an evening walk to a park 4 kilometres from his home. As it was drizzling outside, he tied the dog up and went for the walk alone. The dog managed to untie itself in 20 minutes and started running towards the park. How far from the park (in m) did the dog meet Pushkin if the dog and Pushkin were moving at 5 km/h and 3 km/h, respectively?
Solution Answer: 1500

In 20 minutes Pushkin walks 3 × ⅓ = 1 km. The dog closes this gap at 5 − 3 = 2 km/h, which takes ½ hour.

In that time the dog runs 2.5 km from home, so they meet 4 − 2.5 = 1.5 km = 1500 m from the park.

Q30MCQ
A furniture company, Lakdi Waale, produces chairs (x) and tables (y). The total cost C (in rupees) is given by
C(x, y) = 500x2 + 1000y2 − 1000xy + 40000
Due to a labour contract, the total number of items produced must be exactly 80 units. Calculate the minimum production cost.
ARs. 8,00,000
BRs. 7,20,000
CRs. 6,80,000
DRs. 6,40,000
Solution Answer: C

Substitute y = 80 − x: C = 500x2 + 1000(80 − x)2 − 1000x(80 − x) + 40000 = 2500x2 − 240000x + 6440000.

The minimum is at x = 240000/5000 = 48 (so y = 32). C = 2500 × 2304 − 240000 × 48 + 6440000 = 680000.

Minimum cost = Rs. 6,80,000.

Day 32 complete! 🔥
0 / 90

Correct: 0 · Wrong: 0 · Accuracy: 0%

Keep the streak alive. See you tomorrow for Day 33.

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