IIFT 2017 Question Paper

Since PQ and PT are tangent on circle so $$\angle$$PQO = $$\angle$$PTO = 90

In quadrilateral PQOT   $$\angle$$PQO+$$\angle$$PTO+$$\angle$$QOT+$$\angle$$TPQ = 360

                                                           90+90+$$\angle$$QOT+55 =360

                                                           $$\angle$$QOT = 125

Since AB touches the circle hence OA and OB are the angle bisector of $$\angle$$QOS and $$\angle$$TOS respectively.

                                 So $$\angle$$AOB = $$\frac{1}{2}\angle$$QOT = $$\frac{125}{2}$$ = 62.5

  Given that $$\triangle$$ABC

Since AD is the median to BC, D will be mid point of BC. So coordinates of D = ($$\frac{-2+0}{2} ,\frac{3-4}{2}$$) = (-1 ,$$\frac{-1}{2}$$)

Equation of line passing through points A(1,5) and D(-1,$$\frac{-1}{2}$$) will be :

                $$(y-x_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})$$                   (Here $$(x_{1},y_{1})=(1,5)$$ ,  $$(x_{2},y_{2})=(-1,\frac{-1}{2})$$)
                
                $$(y-5)=\frac{(\frac{-1}{2})-(5)}{(-1)-(1)}(x-1)$$
                
                $$4(y-5)=11(x-1)$$
                
                $$11x-4y+9=0$$

Let's assume that quantities of juice taken from the first and second cans be x and y respectively.

So we can say that  x+y = 12                                                                             ...(1)

Net quantity of water in resulting mixture =$$\frac{25}{100}*x+\frac{50}{100}*y$$

Ratio of water to pulp in resulting mixture = 3:5 hence the mixture will contain $$\frac{3}{3+5}th=\frac{3}{8}th$$ part as water.

                                  $$\frac{25}{100}*x+\frac{50}{100}*y=\frac{3}{8}*(x+y)$$

                                  $$\frac{x}{4}+\frac{y}{2}=\frac{3}{8}*(12)$$    (Since x+y=12 )

                                     $$x+2y=18$$                                                                 ...(2)

                   Solving equation (1) and (2) for x and y 

                                                x=6 , y=6

Let the time taken by second bore well be t hours, then the time taken by first bore well will be t + 10 and the time taken by the third bore well will be t - 8. Now since first two bore wells operating together take same time as taken by the third bore well we can say that work done in unit time will be same in both cases :

$$\frac{1}{t+10}+\frac{1}{t}=\frac{1}{t-8}$$

$$\frac{(t)+(t+10)}{(t)(t+10)}=\frac{1}{t-8}$$

$$(2t+10)(t-8)=(t)(t+10)$$

$$t^{2}-16t-80=0$$

$$(t-20)(t+4)=0$$

Since t $$\neq$$ 4, hence t = 20

So the time taken by the third bore well will be t - 8 = 20 - 8 =12 hours

Average export for the period 2012-2016 = (Sum of all exports in 2012-2016)/5 = (275+350+325+275+250)/5 =295    (US dollar in billions)

Manufactures Export of India in 2016 = 75 percent of the exports (from graph) = (295*75)/100 = 221.25    (US dollar in billions) 

Trade balance = Imports - Exports 

For 2012:

Manufactures Trade balance = Manufactures import - manufactures export

                                           = 500*(35/100) - 275*(65/100) = -3.75                                                                       (From Graph)

For 2013:

Manufactures Trade balance = 475*(40/100) - 350*(60/100) =  -20

For 2014:

Manufactures Trade balance = 450*(45/100) - 325*(55/100) = 23.75

For 2015:

Manufactures Trade balance = 375*(50/100) - 275*(70/100) = -5

For 2016:

Manufactures Trade balance = 350*(55/100) - 250*(75/100) = 5

Number of positive trade balances = 2

Number of negative trade balances = 3

Proportion of positive and negative trade balances = 2:3

Trade deficit of fuel = import of the fuel - export of the fuel = total import * percentage of fuel import -  total import * percentage of fuel export

For year 2013, trade deficit of fuel = (475*42)/100 - (350*25)/100 = 199.50 - 87.5 = 112     (US dollar in billions)

For year 2014, trade deficit of fuel = (450*40)/100 - (325*20)/100 = 180 - 65 =115   (US dollars in billions)

For year 2015, trade deficit of fuel = (375*30)/100 - (275*10)/100 = 112.50 - 27.5 = 85      (US dollars in billions)

For year 2016, trade deficit of fuel = (350*25)/100 - (250*10)/100 = 87.5 - 25 = 62.5       (US dollars in billions)

Trade deficit of fuel is 2nd lowest for year 2015.

India's import in 2017 = import in 2016*(1 +  (10/100))                  (Since growth rate is 10 percent)

                                =  350 * 1.1 = 385    (USD in billions)

India's export in 2017 = export in 2016*(1 +  (10/100))                  (Since growth rate is 10 percent)

                                = 250*1.1 = 275      (USD in billions)

New sectoral share of fuel in imports = 25+5 =30 percent

New sectoral share of fuel in exports = 10+5 =15 percent

India's fuel imports in 2017 = 385*30/100 = 115.5 (USD in billion)

India's fuel exports in 2017 = 275*15/100 = 41.25 (USD in billion)

Trade deficit of fuel = Fuel import - fuel export = 115.5 - 41.25 = 74.25 (USD in billions) 

Trade deficit = Import - Export 

India' trade deficit in 2016 = 350 - 250 = 100   (USD in billions)

India' trade deficit in 2017 = 100+54 = 154  (USD in billions)

154 = Import - 324 

Hence, import = 324+154 = 478 (USD in billions)

India food import percentage in 2017 = India food import percentage in 2016  = 7.5 (Given)

India food import percentage in 2017 = India food import percentage in 2016  = 25 (Given)

India's food export in 2017 = 478*7.5/100 = 35.85 = 36(Approx)     (USD in billion)

India's fuel export in 2017 = 478*25/100 = 119.5       (USD in billion)

The Prices of wheat has increased only in 4 instances. 
January 17 - from Rs.123 to Rs. 137
% increase = 14/123
February 17 - from Rs.137 to Rs.147
% increase = 10/137
May 2017 - from Rs.138 to Rs.146
% increase = 8/138
June 17 -from Rs.146 to Rs. 157
% increase = 11/146

We can see that 8/138 is the smallest fraction and 10/137 is the second smallest fraction. Therefore, the third highest increase in monthly prices happened in February 17 and hence, option B is the right answer.