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Line Charts – Line Chart 4

Directions to Solve

The following line graph gives the percent profit earned by two Companies X and Y during the period 1996 – 2001.

Percentage profit earned by Two Companies X and Y over the Given Years

%Profit = Income – Expenditure/Expenditure x 100

15-3-4-1

1. The incomes of two Companies X and Y in 2000 were in the ratio of 3:4 respectively. What was the respective ratio of their expenditures in 2000 ?
A. 7:22
B. 14:19
C. 15:22
D. 27:35

Answer: Option C

Explanation:

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

2. If the expenditure of Company Y in 1997 was Rs. 220 crores, what was its income in 1997 ?
A. Rs. 312 crores
B. Rs. 297 crores
C. Rs. 283 crores
D. Rs. 275 crores

Answer: Option B

Explanation:

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.


3. If the expenditures of Company X and Y in 1996 were equal and the total income of the two Companies in 1996 was Rs. 342 crores, what was the total profit of the two Companies together in 1996 ? (Profit = Income – Expenditure)
A. Rs. 240 crores
B. Rs. 171 crores
C. Rs. 120 crores
D. Rs. 102 crores

Answer: Option D

Explanation:

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 = (zx)/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.


4. The expenditure of Company X in the year 1998 was Rs. 200 crores and the income of company X in 1998 was the same as its expenditure in 2001. The income of Company X in 2001 was ?
A. Rs. 465 crores
B. Rs. 385 crores
C. Rs. 335 crores
D. Rs. 295 crores

Answer: Option A

Explanation:

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.


5. If the incomes of two Comapanies were equal in 1999, then what was the ratio of expenditure of Company X to that of Company Y in 1999 ?
A. 6:5
B. 5:6
C. 11:6
D. 16:15

Answer: Option D

Explanation:

Let the incomes of each of the two Companies X and Y in 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 = x – E1 x 100     => 50/100 = x – 1     =>     x = 150/100 E1 …. (i)
E1 E1

Also, for Company Y we have:

60 = x – E2 x 100     => 60/100 = x – 1     =>     x = 160/100 E2 …. (ii)
E2 E2

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

150/100 E1 = (160/100) E2     => E1 = 160/150 = 16/15 (Required ratio).
E2

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