IIFT 2009 Question Paper

Caster Seed's yield in the year 2006 = $$\dfrac{135}{106}$$ = 1.273

Groundnut's yield in the year 2006 = $$\dfrac{491}{317}$$ = 1.55

Maize's yield in the year 2006 = $$\dfrac{1102}{1004}$$ = 1.097

Sunflower's yield in the year 2006 = $$\dfrac{880}{472}$$ = 1.864

Rice's yield in the year 2006 = $$\dfrac{153}{107}$$ = 1.429

Bazra's yield in the year 2006 = $$\dfrac{2172}{4992}$$ =0.435

Top 3 yields in 2006: Sunflower,Groundnut,Rice

Moth's yield in the year 2008 = $$\dfrac{250}{1199}$$ = 0.2083

Sesamum's yield in the year 2008 = $$\dfrac{70}{280}$$ = 0.25 

Millets's yield in the year 2008 = $$\dfrac{4}{15}$$ = 0.266

Moong's yield in the year 2008 = $$\dfrac{260}{725}$$ = 0.358

Arhar's yield in the year 2008 = $$\dfrac{9}{19}$$ = 0.474

Urd's yield in the year 2008 = $$\dfrac{35}{102}$$ = 0.343

Chaula's yield in the year 2008 = $$\dfrac{30}{101}$$ = 0.297

Bottom 3 yields in 2008: Moth, Sesamum, Millets

Productivity is defined as total production per hectare. 
Total productivity of pulses in the year 2006 = $$\frac{130+31+149+13+26+2}{799+124+1228+20+126+5}$$ = $$0.1524$$

Total productivity of pulses in the year 2007 = $$\frac{270+30+191+9+45+3}{751+101+1151+19+110+5}$$ = $$0.2564$$

Total productivity of pulses in the year 2008 = $$\frac{260+35+250+9+30+2}{725+102+1199+19+101+5}$$ = $$0.2724$$

We can see that clearly, Total productivity of pulses in the year 2008 > Total productivity of pulses in the year 2007 >Total productivity of pulses in the year 2006. Hence, statement I is incorrect. Hence, we can reject option A and B.

Productivity of Maize in the year 2006 = $$\dfrac{1102}{1004}$$ = 1.097

Productivity of Maize in the year 2007 = $$\dfrac{1116}{1020}$$ = 1.094

Productivity of Maize in the year 2008 = $$\dfrac{1182}{1101}$$ = 1.073

We can see that productivity is approximately same during the given period for Maize. Hence, statement II is correct. Therefore, we can reject option D.

Thus, we can say that option C is the correct answer. 

Productivity is defined as total production per hectare. 
Total productivity of cereals in the year 2006 = $$\frac{153+173+2172+1102+5}{107+598+4992+1004+16}$$ = $$0.5366$$

Total productivity of cereals in the year 2008 = $$\frac{190+380+3350+1182+4}{110+720+4800+1101+15}$$ = $$0.756$$

We can see that clearly, Total productivity of cereals in the year 2008 > Total productivity of cereals in the year 2006. Hence, statement I is correct. 

Now let us check statement II. 

Total yield of oil seeds in the year 2006 = $$\frac{63+491+856+880+135}{422+317+744+472+106}$$ = $$1.1766$$

Total yield of oil seeds in the year 2008 = $$\frac{70+374+799+699+106}{280+298+650+325+80}$$ = $$1.254$$

We can see that yield of Oil seeds is not on decline. Hence, statement II is incorrect. 

Now let us check statement III. 

Area under Urd production in the year 2006 = 124

Area under Urd production in the year 2008 = 102

Total Urd production in the year 2006 = 31

Total Urd production in the year 2008 = 35

Urd's yield in the year 2006 = $$\frac{31}{124}$$ = 0.25

Urd's yield in the year 2008 = $$\frac{35}{102}$$ = 0.34

Hence, we can say that statement III is correct. Therefore, option A is the correct answer. 

Total Oil used in the year 1998 = 22+1012+1732+104 = 2870. 

Therefore, the percentage of total used that is used for House Hold = $$\frac{22}{2870}\times 100$$ = 0.766. 

Similarly we can calculate for remaining year. 

From the table we can see that, in the year 1999 the Oil used for House Hold as a percentage of total Oil Used is highest. Hence, option B is the correct answer.

Total oil produced in the year 1996 = 10+700+1794+104+650 = 3258.

Therefore, oil production loss as a percentage of total oil produced in the year = $$\dfrac{650}{3258}\times 100$$ = 19.95%.

Similarly, we can calculate for the remaining year. Tabulating the same data, 

From the table, we can see that the oil production loss as a percentage of total oil produced is the lowest for the year 2002. Hence, option A is the correct answer. 

Total oil used in the year 1996 = 10+700+1794+104 = 2608.

Therefore, Oil used by Suburban as a proportion of Total Oil Used = $$\dfrac{104}{2608}\times 100$$ = 3.99 percent. 

Similarly, we can calculate for the remaining years. 

From the table, we can see that oil used by suburban as a proportion of total oil used is the highest for the year 2008. Hence, option D is the correct answer. 

Total oil used in the year 1996 = 10+700+1794+104 = 2608.

Total oil produced in the year 1996 = 10+700+1794+104+650 = 3258.

Similarly, we can calculate for the remaining quantities for both the years. Tabulating the same data, 

Therefore, growth rate of total oil used in the year 1997 as compared to 1996 = $$\dfrac{2914-2608}{2608}\times 100$$ = 11.73%

Therefore, growth rate of total oil produced in the year 1997 as compared to 1996 = $$\dfrac{3646-3258}{3258}\times 100$$ = 11.91%

Similarly, we can calculate for the remaining year. Tabulating the same data, 

From the table we can see that, the growth rate in ‘Production of Oil’ is more than the growth rate in ‘Total Oil Used’ in eight years. 
{Year 1996, 1997, 1998, 2003, 2004, 2005, 2006, 2007}. Hence, option D is the correct answer.

Total oil used in the year 1996 = 10+700+1794+104 = 2608.

Total oil produced in the year 1996 = 10+700+1794+104+650 = 3258.

Similarly, we can calculate for the remaining quantities for both the years. Tabulating the same data, 

From the table, we can see that quantity of 'total oil Produced’ is increasing every year since 2003. Hence, option D is the correct answer. 

The first point  tells us that "Paul lives between Som and Krishna".
This gives us an initial thought that these three can occupy the houses 1, 2, 3 in the row with Paul occupying the 2nd house and Som and Krishna sharing houses 1 and 3 in no particular order. In this case Laxman has to occupy the 4th house, i.e. the Yellow house. OR they can occupy the houses 2,3,4 with Paul occupying the 3rd house and Som and Krishna sharing houses 2 and 4 in no particular order. In this case Laxman has to occupy the 1st house, i.e. the Blue house.
However, since we know from point (II) that Laxman does not stay in the Blue house we reject this possibility.
Consequently, we can fix the position of Paul and Laxman in the Green and Yellow houses respectively.

At this point if we use point (VIII), we see that since ԋrishna lives in between two houses he cannot be in the first house. Hence, Krishna takes the third house and Som takes the 1st one.

Thus, the grid converts to:

From this point we need to focus on fixing the values of the salaries of the 4 individuals.
The values of the four salaries can first be identified as 30000, 50000 (from point VIII), 80000 ( point ) and 110000 (point VI). We also know from Point VIII that Krishna lives between the people
earning 30000 and 50000 which means that 30000 and 50000 could be Laxman and Paul's salary.
Further, the salary difference between Laxman and Som being 30000, their salaries would have to be 50000 and 80000, with Laxman getting 50000 and Som getting 80000. Consequently Paul gets 30000 and Krishna would earn 110000. The solution grid would then look like below:

So Krishna lives in Red house