Line Charts Questions & Answers - Page 8

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

Then, 55 = (x - 200)/200 x 100  =>  x = 310

Therefore Expenditure of Company X in 2001 = Income of Company X in 1998

= Rs. 310 crores.

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

Then, 50 = (z - 310)/310 x 100 => z = 465

Therefore Income of Company X in 2001 = Rs. 465 crores.

Let the expenditures of each companies X and Y in 1996 be Rs. x crores.

And let the income of Company X in 1996 be Rs. z crores.

So that the income of Company Y in 1996 = Rs. (342 - z) crores.

Then, for Company X we have:

40 = (z - x)/x x 100  =>  40/100 = z/x - 1  =>  x = 100z/140 .... (i)

Also, for Company Y we have: 45 = ((342 - z)/x) x 100  =>  45/100 = ((342 - z)/x) - 1 => x = ((342 - z) x 100)/145 .... (ii) 

From (i) and (ii), we get:

100z/140 = ((342 - z) x 100)/145 => z = 168

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

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

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

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

Profit percent of Company Y in 1997 = 35.

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

Then, 35 = (x - 220)/220 x 100  =>  x = 297

Therefore Income of Company Y in 1997 = Rs. 297 crores.

Let the incomes in 2000 of Companies X and Y be 3x and 4x respectively.

And let the expenditures in 2000 of Companies X and Y be E₁ and E₂ respectively.

Then, for Company X we have:

65 = (3x - E₁)/E₁ x 100  =>  65/100 = 3x/E₁ - 1  =>  E₁ = 3x x ( 100/165 ) .... (i)

For Company Y we have:

50 = (4x - E₂)/E₂ x 100  =>  50/100 = 4x/E₂ - 1 => E₂ = 4x x ( 100/150 ) .... (ii)

From (i) and (ii), we get:

E₁/E₂ = (3x x ( 100/165 ))/(4x x ( 100/150 )) = (3 x 150)/(4 x 165) = 15/22 (Required ratio)

Required percentage = ( 128000/78000 x 100 ) %

≈ 164%