CAT 1999 Question Paper

Since the increase in imports and exports is at average, the exports and imports in the next 4months will be half of their respective first eight months.

Exports in the first 8 months of 1998-1999 is $21436 so, in the next 4 months it will be 21436/2 = 10718

Total exports= 21346+10718=32154.

Although total imports have been increased the percentage share for all is decreased expect A and G. This means surely one of A and G has the highest increase. 

Percentage growth in exports of country A is (23%*32154 - 19%*33979)/19%*33979 = 14.5%
Percentage growth in exports of country G is (12%*32154 - 10%*33979)/10%*33979 = 13.5 %
Hence, the region to which Indian exports witnessed the highest percentage growth is region A i.e USA

Since the increase in imports and exports is at average, the exports and imports in the next 4months will be half of their respective first eight months.

Exports in first 8 months of 1998-1999 is $21436 so, in next 4 months it will be 21436/2 = 10718

Total exports= 21346+10718=32154.

Similarly, total imports= 28126+ 28126/2 = 42189

Trade deficit = 42189-32064= 10035

Trade deficit in 1997-98= 40779-33979=6800.

Increase = (10035-6800)/6800 = 47.5%

Price change of arhar = (2105-1700)/1700 = 23.82%
Price change of pepper = (19250-18500)/18500 = 4.05%
Price change of sugar = (1430 - 1440)/1430 = -0.69%
Price change of gold = (3850 - 4250)/3850 = -9.41%

Hence, the price change is maximum for arhar.

Volatility for arhar is (2300-1500)/1900 = 42%
Volatility for pepper is (19500-17500)/18500 = 10.8%
Volatility for sugar is (1500-1410)/1450 = 6.2%
Volatility for gold is (4300-3800)/4050 = 12%

Hence, the volatility is least for sugar.

The profit percentage equals 25%*(2105/1700-1) + 25%*(19250/18500-1) + 25%*(1430/1440-1) + 25%*(3850/4250-1)
This equals 25%*(23.82% + 4.05% -0.69% - 9.41%) = 25%*17.77 = 4.4%

The closest option to this is option (d)

Volatility for arhar is (2300-1500)/1900 = 42%
Volatility for pepper is (19500-17500)/18500 = 10.8%
Volatility for sugar is (1500-1410)/1450 = 6.2%
Volatility for gold is (4300-3800)/4150 = 12%

Hence, the highest volatility is around 40%

Bangladesh has the highest percentage in drinking water facilities. Let us see which countries it dominates. This is possible if it has greater sanitation facilities also as compared to the other country.

Bangladesh has better sanitation facilities than India, China, Pakistan and Nepal. So those Bangladesh dominates those four countries and they are not on the coverage frontier.

Similarly, Philippines has the highest percentage of sanitation facilities. Let us see which countries it dominates. This is possible if it has greater drinking water coverage also.

Philippines has greater drinking water coverage than all countries except Bangladesh. Hence, it dominates all the countries except Bangladesh. So, no other country is on the coverage frontier.

Hence, the only countries on the coverage frontier are Bangladesh and Philippines.

India has lesser sanitation facilities than Pakistan. Hence it is false that India > Pakistan. So statement A is false.

India has greater sanitation facilities as well as drinking water coverage than China. Similar is the case between India and Nepal.
Hence, India > China and India > Nepal. So, statement B is true.

Sri Lanka has lesser drinking water coverage than China. Hence, statement C is false.

China has greater sanitation facilities as well as drinking water coverage than Nepal. Hence, China > Nepal and statement D is true.

So, the only two true statements are B and D.

Let total rural population in India be R and urban population in India be U.

Total population in India = T = U + R

Based on the sanitation facilities table, 

$$\frac{70}{100}$$ U + $$\frac{14}{100}$$ R = $$\frac{29}{100}$$(U + R)

Solving, we get

$$\frac{U}{R}$$ = $$\frac{15}{41}$$

U : R = 15 : 41

Rural population % = $$\frac{41}{15+41}\times\ 100$$ = $$\frac{41}{56}\times\ 100$$ = 73.2%

Let total rural population in China be A and urban population in China be B.

Total population in India = T = A + B

Based on the sanitation facilities table,

$$\frac{74}{100}$$ B + $$\frac{7}{100}$$ A = $$\frac{24}{100}$$(A + B)

Solving, we get

$$\frac{A}{B}$$ = $$\frac{50}{17}$$

A : B = 50 : 17

Rural population % = $$\frac{50}{50+17}\times\ 100$$ = $$\frac{50}{67}\times\ 100$$ = 74.6%

Let total rural population in Indonesia be C and urban population in Indonesia be D.

Total population in India = T = C + D

Based on the sanitation facilities table,

$$\frac{40}{100}$$ C + $$\frac{73}{100}$$ D = $$\frac{51}{100}$$(C + D)

Solving, we get

$$\frac{C}{D}$$ = $$\frac{22}{11}$$

C : D = 2 : 1

Rural population % = $$\frac{2}{2+1}\times\ 100$$ = $$\frac{2}{3}\times\ 100$$ = 66.7%

Let total rural population in Philippines be R and urban population in Philippines be U.

Total population in India = T = R + U

Based on the sanitation facilities table,

$$\frac{88}{100}$$ U + $$\frac{66}{100}$$ R = $$\frac{77}{100}$$(U + R)

Solving, we get

$$\frac{U}{R}$$ = $$\frac{11}{11}$$

U : R = 1 : 1

Rural population % = $$\frac{1}{1 + 1}\times\ 100$$ = $$\frac{1}{2}\times\ 100$$ = 50%

Ascending order: Philippines, Indonesia, China

Therefore, answer is option A.