LINE-GRAPHS

Ans .

112.5%

1. Explanation :

   Required percentage = [(405/360)*100] % = 112.5 %

Ans .

381

1. Explanation :

   Average marks obtained in all the periodical exams.

   = (1/6)*[360+370+385+400+404] = 380.83 = 381.

Ans .

78.75%

1. Explanation :

   Required percentage = [(370+385)/(500+500) * 100] % = [(755/1000)*100]% =75.5%

Ans .

none

1. Explanation :

   As is clear from graph, the total marks obtained in periodical exams, go on increasing.

   Since, the maximum marks for all the periodical exams are same , it implies that the percentage of marks also goes on increasing. Thus,

   in none of the periodical exams, there is a fall in percentage of marks compared to the previous exam.

Ans .

Oct. 01

1. Explanation :

   Percentage increases in marks in various periodical exams compared to the previous exams are:

   For Jun. 01 = [(365-360)/360 * 100 ] % = 1.39 %

   For Aug. 01 = [(370-365)/365 * 100 ] % = 1.37 %

   For Oct. 01 = [(385-370)/370 * 100 ] % = 4.05%

   For Dec. 01 = [(400-385)/385 * 100 ] % = 3.90 %

   For Feb. 02 = [(405-400)/400 * 100 ] % = 1.25 %

Ans .

4

1. Explanation :

   The exports are more than the imports implies that the ratio of value of imports to exports is less than 1.

   Now, this ratio is less than 1 in the years 1995,1996,1997 and 2000. Thus, there are four such years.

Ans .

1997

1. Explanation :

   The imports are minimum proportionate to the exports implies that the ratio of the

   value of imports to exports has the minimum value.

   Now, this ratio has a minimum value of 0.35 in 1997, i.e., the imports are minimum proportionate to the exports in 1997.

Ans .

b.Rs.320 crores

1. Explanation :

   Ratio of imports to exports in the years 1996=0.85.

   Let the exports in 1996=Rs.320 crores.

   Then,272/x =0.85 implies x=272/.85 = 320..

Ans .

Data inadequate

1. Explanation :

   The graph gives only the ratio of imports to exports for different

   years. To find the percentage increase in imports from 1997 to 1998, we require more details such as the

   value of imports or exports during these years. Hence, the data is inadequate to answer this question.

Ans .

d.Rs 420 crores

1. Explanation :

   The ratio of imports to exports for the years 1998 and 1999 are 1.25 and 1.40 respectively.

   Let the exports in the year 1998 = Rs. x crores

   Then, the exports in the year 1999=Rs(500-x) crores.

   1.25=250/x implies x=250/1.25=200

   Thus the exports in the year 1999=Rs. (500-200)crores=Rs.300 crores

   Let the imports in the year 1999=Rs. y crores

   Then, 1.4=y/300 implies y=(300*1.4)=420.

   Imports in the year 1999=Rs.420 crores..

Ans .

26000

1. Explanation :

   Total production of Company X from 1997 to 2002

   = 119000+99000+141000+78000+120000+159000 = 716000

   and total production of Company Y from 1997 to 2002

   =139000+120000+100000+128000+107000+148000=742000

   Difference=742000-716000=26000.

Ans .

21000

1. Explanation :

   Require difference = 128000-107000 = 21000.

Ans .

119333

1. Explanation :

   Average number of vehicles manufactured by Company X

   = (91/6)* (119000 + 99000 + 141000 + 78000 + 120000 + 159000) = 119333.

Ans .

2000

1. Explanation :

   The difference between the production of Companies X and Y in various years are.

   For 1997 = (139000 -119000) = 20000;

   For 1998 = (120000 -99000) = 21000;

   For 1999 = (141000 -100000) = 41000;

   For 2000 = (128000 -78000) = 50000;

   For 2001 = (120000 -107000) = 13000;

   For 2003 = (159000 -148000) = 11000;

   Clearly, maximum difference was in 2000

Ans .

164

1. Explanation :

   Required percentage = [( 128000/78000)* 100] % = 164 %.

Ans .

(b). Rs. 297 crores

1. Explanation :

   Profit percent ofcompany Y in 1997=35.

   Let the income of company Y in 1997 be Rs.x crores

   Then,35 = \(\frac{x-220}{220}\) X 100 =>x =297

   Income of company Yin 1997 = Rs.297crores.

Ans .

16:15

1. Explanation :

   Let the incomes of the twocompanies X and Yin 1999 be Rs.x and let the

   Expenditures of companies X and Y in 1999 be E1 and E2 respectively

   Then, for Company X we have:

   50= \(\frac{x-E1}{E1}\) x 100 => \(\frac{50}{100}\) = \(\frac{x}{E1}\) -1 => x = \(\frac{150}{100}\) E1

   Also, for the Company Y we have:

   60 = \(\frac{x-E2}{E2}\) *100 =>\(\frac{60}{100}\) = \(\frac{x}{E2}\) -1 =>x = \(\frac{160}{100}\) E2

   From (i) and (ii),we get

   \(\frac{150}{100}\) E1=\(\frac{160}{100}\) E2 => \(\frac{E1}{E2}\) = \(\frac{160}{150}\)= \(\frac{16}{15}\)(Required ratio).

Ans .

15:22

1. Explanation :

   Let the incomes in 2000 of companies X and Y be 3x and 4x respectively.And let

   the expenditure in 2000 of companies X and Y be E1 and E2 respectively.

   Then, for company X we have:

   65= \(\frac{3x-E1}{E1}\) x 100 => \(\frac{65}{100}\) = \(\frac{3x}{E1}\)-1 =>E1=3x *\(\frac{100}{165}\)

   For company Y we have:

   50 = \(\frac{4x-E2}{E2}\) *100 => \(\frac{50}{100}\) = \(\frac{4x}{E2}\)-1 =>E2 = 4x* \(\frac{100}{150}\)

   From (i)and(ii) we get:

   \(\frac{E1}{E2}\) = \(\frac{3x*(100/165)}{4x*(100/150)}\) =\(\frac{3* 150}{4*165}\) =\(\frac{15}{22}\) (Required ratio)

Ans .

Rs.102crores

1. Explanation :

   Let the expenditures of each of the Companies X and Y in 1996 be

   Rs.xcrores.And let the income of Company X in 1996 be Rs.zcrores so that the income of Company Y in 1996 =Rs.(342-z)crores.

   Then,for company X we have:

   40= \(\frac{z-x}{x}\) *100 => \(\frac{40}{100}\) =\(\frac{ z}{x}\) -1 => x = \(\frac{100z}{140}\)

   Also for company Y we have:

   45= \(\frac{(342-z)-x}{x}\) *100 => \(\frac{45}{100}\)= \(\frac{ (342-z)}{x}\) -1 =>x = \(\frac{(342 –z)}{145}\)* 100

   From(i)and (ii) we get:

   \(\frac{100z}{140}\) = \(\frac{(342-z)*100}{145}\) =>z = 168

   Substituting z=168 in (i),we get: x=120

   Total expenditure of companies X and Y in 1996=2x=Rs.240crores.

   Total income of companies X and Y in 1996=Rs.342 crores.

   Total profit =Rs.(342-240)crores =Rs.102 crores

Ans .

Rs.465crores

1. Explanation :

   Let the income of company X in 1998 be Rs.x crores.

   Then,55= \(\frac{x-200}{200}\) *100 => x = 310.

   Expenditure of Company X in 2001= Income of company X in 1998 = Rs.310crores

   Let the income of company X in 2001 be Rs.z crores

   Then,50 = \(\frac{z-310}{310}\) *100 =>z = 465.

   Income of company X in 2001 = Rs.465 crores.