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HURDLE-17 : LINEAR EQUATIONS. FIXED COST & VARIABLE COST

(Solve this Hurdle by 8th April)

Q1. The cost per head of joining a school picnic party is partly fixed and partly vary linearly depending upon number of students who join the picnic. If 30 students join the party the expense per head is Rs. 5,900. If the number of students is increased to 45 the expense per head is Rs 5,600. Which of the following statement/s is/are false :
1) The cost per head will reduce as the number of students increase.
2) The cost per head will increase as the number of students increase.
3) The minimum possible cost per head is more than Rs 5000.
4) The maximum possible cost per head is Rs. 32,000.

Q2. The hostel expenses of a MBA institute is partly fixed and partly vary linearly, depending upon number of students in the hostel. If 34 students stay at the hostel the expense per head is Rs. 8,360. If the number of students is increased to 48 the expense per head is Rs 7,905. Which of the following statement/s is/are true:
1) If the number of students is 65 the cost per head will be Rs 7,616.
2) If the number of students is 100 the cost per head will be Rs. 7500. (UrPercentile.com)
3) The minimum cost possible cost per head will be more than 6500.
4) The maximum possible cost per head is less than 62,000.


Q3. The cost of manufacturing a dinning table is partly fixed and partly vary linearly, depending upon number of tables manufactured. If 36 tables are manufactured the manufacturing cost per table is Rs. 8,110. If the number of tables manufactured is increased to 52 the cost per table is reduced to Rs 7,830. Now select the best option based on following two statements :
1) No matter how many tables you manufacture the minimum you have to pay per table will be more than 7200 for each.
2) If you manufacture 70 tables you will have to pay Rs 7,668 per table.
Option 1 : Both statements are true
Option 2 : Both statements are false
Option 3: Only statement 1 is true
Option 4 : Only statement 2 is true.

Q4. The cost of traveling between two cities by a certain train is partly fixed and partly vary linearly, depending upon number of passengers traveling . If the number of passengers is 380, the cost is Rs. 8,425. If the number of passengers is increased to 550, the traveling cost is Rs 8,170. How much would be the cost if the number of passengers is 750 ?

Q5. The cost per head of joining a club is partly fixed and partly vary linearly depending upon number of students who join the club. If 40 students join the club the expense per head is Rs.9,160. If the number of students is increased to 58 the expense per head is Rs 8,800. (UrPercentile.com) How much would be the expense per head if the number of student is further increased to 80 ?

Q6. The hostel expenses of a MBA institute is partly fixed and partly vary linearly, depending upon number of students in the hostel. If 42 students stay at the hostel the expense per head is Rs. 14,635. If the number of students is increased to 62 the expense per head is Rs 13,785. How much would be the expense per head if the number of student is further increased to 85 ?

Q7. The cost of manufacturing a washing machine is partly fixed and partly vary linearly, depending upon number of machines manufactured. If 44 machines are manufactured the manufacturing cost per machine is Rs. 12,985. If the number of machines manufactured is increased to 65 the cost per machine is reduced to Rs 12,796. How much would be the cost of manufacturing per machine if the number of machines manufactured is further increased to 90 ?

Q8. The cost of traveling between two cities by a certain train is partly fixed and partly vary linearly, depending upon number of passengers traveling . If the number of passengers is 460, the cost is Rs. 23,000. If the number of passengers is increased to 680, the traveling cost is Rs 21,955. How much would be the cost if the number of passengers is 950 ?

Q9. The cost per head of joining a school picnic party to Nepal is partly fixed and partly vary linearly depending upon number of students who join the picnic. (UrPercentile.com) If 48 students join the party the expense per head is Rs. 21,945. If the number of students is increased to 71 the expense per head is Rs 21,370. How much would be the expense per head if the number of student is further increased to 100 ?

Q10. The hostel expenses of a Medical institute is partly fixed and partly vary linearly, depending upon number of students in the hostel. If 50 students stay at the hostel the expense per head is Rs. 13,554. If the number of students is increased to 74 the expense per head is Rs 13,050. How much would be the expense per head if the number of student is further increased to 105 ?

Q11. The cost of manufacturing dinning tables is partly fixed and partly vary linearly, depending upon number of tables
manufactured. If 24 tables are manufactured the manufacturing cost per table is Rs. 16,635. If the number of tables
manufactured is increased to 77 the cost per table is reduced to Rs 13,720. How much would be the cost of manufacturing per table if the number of tables manufactured is further increased to 110 ?

Q12. The cost of traveling between two cities by a certain train is partly fixed and partly vary linearly, depending upon number of passengers traveling . If the number of passengers is 280, the cost is Rs. 10,120. If the number of passengers is increased to 600, the traveling cost is Rs 9,880. How much would be the cost if the number of passengers is 750 ?

Q13. The cost per head of joining a school picnic party is partly fixed and partly vary linearly depending upon number of students who join the picnic. If 56 students join the party the expense per head is Rs. 15,690. If the number of students is increased to 83 the expense per head is Rs 14,880. How much would be the expense per head if the number of student is further increased to 120 ?

Q14. The hostel expenses of a MBA institute is partly fixed and partly vary linearly, depending upon number of students in the hostel. If 32 students stay at the hostel the expense per head is Rs. 14,375. If the number of students is increased to 86 the expense per head is Rs 11,000. How much would be the expense per head if the number of student is further increased to 125 ?

Q15. The cost of manufacturing a dinning table is partly fixed and partly vary linearly, depending upon number of tables manufactured. If 56 tables are manufactured the manufacturing cost per table is Rs. 17,535. If the number of tables manufactured is increased to 89 the cost per table is reduced to Rs 15,390. How much would be the cost of manufacturing per table if the number of tables manufactured is further increased to 130 ?

Q16. The cost of traveling between two cities by a certain train is partly fixed and partly vary linearly, depending upon number of passengers traveling . If the number of passengers is 550, the cost is Rs. 13,984. If the number of passengers is increased to 920, the traveling cost is Rs 12,985. How much would be the cost if the number of passengers is 1350 ?

Q17. The cost per head of joining a school picnic party is partly fixed and partly vary linearly depending upon number of students who join the picnic. If 65 students join the party the expense per head is Rs. 13,076. If the number of students is decreased to 42 the expense per head is Rs 13,720. How much would be the expense per head if the number of student is further increased to 140 ?


Q18. The hostel expenses of a MBA institute is partly fixed and partly vary linearly, depending upon number of students in the hostel. If 66 students stay at the hostel the expense per head is Rs. 14,830. If the number of students is reduced to 46 the expense per head is Rs 15,930. How much would be the expense per head if the number of student is further increased to 110 ?

Q19. The cost of manufacturing a dinning table is partly fixed and partly vary linearly, depending upon number of tables
manufactured. If 34 tables are manufactured the manufacturing cost per table is Rs. 14,540. If the number of tables
manufactured is reduced to 32 the cost per table is reduced to Rs 14,655. How much would be the cost of manufacturing per table if the number of tables manufactured is further increased to 115 ?

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MATCH THE WORDS IN SET A WITH THEIR MEANINGS IN SET B

SET A: 20. Importunate 21. Exiguous, 22. Intramural, 23. Percolate, 24. Rotund 25. Obsolescence

SET B:
A. Plumpness.
B. Gloomy.
C. Gradually falling into disuse.
D. A ill mannered person.
E. Calling names
F. Small, minute, meager.
G. To regret.
H. Reduce the strength , weaken.
I. Within the walls of a city.
J. To filter.
K. Being full of life and high sprits.
L. To Punish.
M. Urging or demanding in troublesome manner.
N. Fragments.

++++++++++++++++++++++++++++++++++++++

Q26 .Read the article ( Price hike in the pipeline) below and write summary in 150 words.

Source : The Hindu

Price hike in the pipeline

OUTSOURCING an intractable problem to an "expert" committee is often the preferred choice of governments. Doing this enables governments to maintain the pretence of obtaining an independent, objective assessment, while actually pursuing a predetermined but controversial course.

The United Progressive Alliance (UPA) government has repeatedly threatened to increase fuel prices but has been restrained by its Left allies. The government can now cite the recent report of the Committee on Pricing and Taxation of Petroleum Products headed by C. Rangarajan, Chairman of the Prime Minister's Economic Advisory Council, to justify its trigger-happy intentions.

It would appear that the sharp increase in international crude oil prices, from about $40 a barrel in late 2004 to the current level of more than $60 a barrel, leaves the government with no other option but to increase prices. But arranging the facts in this manner only obfuscates matters. Obviously, if the prices of petroleum products are to be kept in check, because they are a basic raw material for the economy and in order to protect consumers, other options have to be considered instead of pleading helplessness in the face of buoyant prices in the international market. The Rangarajan Committee, instead of correcting systemic anomalies, merely attempts to fine-tune a badly flawed regime.

The overarching importance given to the mantra of "revenue neutrality", a critical ingredient of fiscal fundamentalism, tied the hands of the committee in its search for a solution. The government's excessive reliance on the petroleum sector for revenues explains its unwillingness to consider options that would be obvious to many. In 2004-05, almost one-fourth of the customs duty collections amounting to Rs.56,000 crores came from the petroleum sector; moreover, 43 per cent of all excise duty collections, amounting to Rs.1,00,720 crores, came from levies on the petroleum sector.

There is much truth in the "no gain without pain" principle. If consumers - or the economy at large - are to be given relief, the government needs necessarily to forgo revenue collections. The "revenue neutrality" principle closes this option. Although customs and excise duties have been cut in the last few years, the increase in prices and the increase in the consumption of petroleum products have resulted in the government mobilising an increasing proportion of its revenue from this sector. Indeed, the perverse logic of the situation is such that the government would actually welcome an increase in prices simply because it would gain more revenues.

The Rangarajan Committee points out that the sharp increase in the prices of "sensitive petroleum products" such as liquefied petroleum gas (LPG) and kerosene, distributed through the Public Distribution System (PDS) has resulted in subsidies climbing to "unprecedented levels". The panel observes that the subsidies on these two key cooking fuels amount to Rs.26,000 crores-Rs.15,000 crores for kerosene and Rs.11,000 crores for LPG. Since the government finances only 13 per cent of the LPG subsidy through its Budget, the burden of the subsidy has fallen on public sector oil companies. The panel observes that this not only leads to a fiscal problem but affects the vitality of the publicly owned companies involved in oil exploration, refining and marketing. Since oil prices are unlikely to soften in the near future, the panel said "an immediate adjustment of prices and subsidies is an immediate imperative".

Targeting, that familiar device of choice of the subsidy-bashers, is recommended as a means of slashing the subsidy on kerosene, the main fuel of the poor. Making only those families below the poverty line (BPL) eligible for subsidised kerosene would result in the kerosene subsidy being slashed by about 40 per cent.

In fact, the hardline stance of the committee is surprising and potentially controversial. It mandates that the Planning Commission's controversial criteria for the identification of BPL families, instead of those based on enumeration by State governments, will prevail in identifying families that will be able to avail themselves of the kerosene subsidy. This is sure to raise a controversy.

The committee also views the removal of the LPG subsidy as an "urgent imperative". It suggests that "an immediate one-time" hike of Rs.75 a cylinder is necessary and that this needs to be followed up by regular revisions to close the gap between subsidised and actual prices, now amounting to Rs.171 a cylinder. It reckons that its suggestions on targeting and cutting subsidies will reduce the bill by almost Rs.11,000 crores.

Most people would be aghast if they understood how petroleum prices are actually set in India. India is self-sufficient in refining crude oil for conversion to petroleum products. Since the dismantling of the administered pricing mechanism (APM) in 2002, prices are determined using the import parity principle. This is a purely notional price, arrived at on the basis of the assumption that petroleum products are imported. The notional price includes the free onboard price, ocean freight, insurance, exchange rates, customs duties, losses during transit, and port charges. Further, the retail selling price that consumers pay includes the cost of transport from the depot to the retail outlet, the marketing cost, the margins of the oil companies, State-specific taxes and duties, dealers' commissions and other charges. As the accompanying graphic shows, taxes, duties and levies of the Central and State governments account for more than half the retail selling price that consumers pay for fuels.

The Parliamentary Standing Committee on Petroleum and Natural Gas, which evaluated the import parity system of pricing, observed in its report of August 2005 that it "artificially inflates the price of petroleum products." It pointed out that the system was "irrational and far-removed from reality" because prices were arrived at on the basis of "assumed costs". It urged the government "to scrap the method" and adopt "a more realistic method". The import parity principle, in effect, enables Indian refining companies to import inflated prices which bear no relation to the actual cost of production in the country. The sharp increase in international crude oil prices has enabled Indian refiners to earn a bonanza.

However, the oil-marketing companies, particularly the public sector companies Hindustan Petroleum Corporation Ltd (HPCL) and Bharat Petroleum Corporation Ltd (BPCL), are at a disadvantage because they have small refining capacities. The biggest gainer was obviously Reliance Industries, whose stand-alone refinery with a capacity of 33 million tonnes a year is the biggest refinery in India.

The notional method of pricing petroleum products obviously overstates the "losses" of the public sector oil companies. It is important to differentiate between losses and "under-recoveries" of the oil companies. The latter is purely notional since they relate to the notional price that the companies could charge if they were free to do so. Actual losses, on the other hand, are real. The confusion deliberately created by the free interchange of the two terms in much of the financial media makes the situation appear far more alarming than it actually is. The Rangarajan Committee estimated that the "under-recoveries" of the oil companies will amount to Rs.39,704 crores in 2005-06. But the actual losses amount to only about Rs.3,000 crores, mainly confined to three public sector oil-marketing companies, HPCL, BPCL and IBP.

Reliance enjoys several advantages that are not available to the public sector companies. First, since it does not have to sell subsidised LPG or kerosene through the PDS there is no question of making losses on such operations. Secondly, it does not have to pay cess on crude oil unlike public sector oil exploration companies such as the Oil and Natural Gas Corporation (ONGC) and Oil India Ltd. In fact, the recent Union Budget increased the cess on crude from Rs.1,800 a tonne to Rs.2,500 a tonne. Simple calculations show that the cess at the new level amounts to $7.77 a barrel. This implies that the cess that ONGC, the principal oil exploration company in India, will have to pay is about 13 per cent of the international price of crude oil, a margin that would wreck any commercial undertaking. One wonders what would happen if the cess is hiked to Rs.4,800 a tonne, as has been recommended by the Rangarajan Committee. Since the New Exploration Licensing Policy (NELP) spares private oil exploration companies from the cess, an increase in the cess skews the field even more for ONGC vis-a-vis the private players.

Thirdly, Reliance, unlike the public sector oil companies, exports nearly one-third of its refined output and in doing this enjoys substantial tax benefits. For instance, the parliamentary committee's report showed that the government spent nearly Rs.2,700 crores in 2004-05 on advance licence benefits, a subsidy for exporters. Reliance, by virtue of being by far the biggest exporter of petroleum products - it exported one-third of its output in 2004-05 - was the biggest beneficiary of this subsidy: it received almost 60 per cent of the subsidy that was paid by the government to exporters of petroleum products. Kerosene and LPG consumers can well ask why the government wants to cut subsidies on the major cooking fuels ruthlessly when the biggest private exporter is provided incentives to export.

Dipankar Mukherjee, a member of the Parliamentary Standing Committee and widely regarded as the Left's expert on the petroleum sector, asks: "Why has the government ignored the recommendations of the parliamentary committee? Is it of a lesser value than the Rangarajan report?" He pointed out that the three main "stake-holders" - public sector oil companies, the government and consumers - found no representation in the Rangarajan Committee. "The imprint of the Finance Ministry can be clearly seen in the committee's outlook and its recommendations," he observed.

It is obvious that political compulsions, particularly forthcoming elections in several States, have restrained the Finance Ministry acting immediately on the panel's recommendations. But consumers can be sure that when these are out of the way, and when Parliament is not in session, prices will be set ablaze again.

Answers of Above Hurdle-17
Following are the answers and solutions of Hurdle 17 followed by solutions
Hurdle 17-Answers

  Hurdle 18 :Distance ,Time & Speed
Q1 to Q6 are compulsory. Attempt any 6 out of Q7 to Q18. Q19 to Q29 are compulsory.
Hurdle18.htm
  Links of Hurdle 31 to 78
Links of Hurdle 31 to 78 will be available only to the closed community of Urpercentile members.

Hurdle31onwards.htm
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