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Line Charts – Line Chart 6

Directions to Solve

The following line graph gives the annual percent profit earned by a Company during the period 1995 – 2000.

Percent Profit Earned by a Company Over the Years.

%Profit = Income – Expenditure x 100
Expenditure

15-3-6-1

1. If the expenditures in 1996 and 1999 are equal, then the approximate ratio of the income in 1996 and 1999 respectively is?
A. 1:1
B. 2:3
C. 13:14
D. 9:10

Answer: Option D

Explanation:

Let the expenditure in 1996 = x.

Also, let the incomes in 1996 and 1999 be I1 and I2 respectively.

Then, for the year 1996, we have:

55 = (I1x)/x x 100   => 55/100 = I1 – 1   =>   I1 = 155x/100 … (i)
x
70 = (I2x)/x x 100   => 70 = I2 – 1   =>   I2 = 170x/100 … (ii)
100 x

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

I1 =
( 155x/100 )
= 155 => 0.91 => 9 : 10.
I2
( 170x/100 )
170

2. If the income in 1998 was Rs. 264 crores, what was the expenditure in 1998?
A. Rs. 104 crores
B. Rs. 145 crores
C. Rs. 160 crores
D. Rs. 185 crores

Answer: Option C

Explanation:

Let the expenditure is 1998 be Rs. x crores.

Then, 65 = (264 – x)/x x 100
=> 65/100 = 264/x – 1
=>   x = (264 x 100)/165 = 160.

Therefore Expenditure in 1998 = Rs. 160 crores.


3. In which year is the expenditure minimum?
A. 2000
B. 1997
C. 1996
D. Cannot be determined

Answer: Option D

Explanation:

The line-graph gives the comparison of percent profit for different years bu the comparison of the expenditures is not possible without more data.Therefore, the year with minimum expenditure cannot be determined.


4. If the profit in 1999 was Rs. 4 crores, what was the profit in 2000?
A. Rs. 4.2 crores
B. Rs. 6.6 crores
C. Rs. 6.8 crores
D. Cannot be determined

Answer: Option D

Explanation:

From the line-graph we obtain information about the percentage profit only. To find the profit in 2000 we must have the data for the income or expenditure in 2000.

Therefore, the profit for 2000 cannot be determined.


5. What is the average profit earned for the given years?
A. 50(2/3)
B. 55(5/6)
C. 60(1/6)
D. 335

Answer: Option B

Explanation:

Average percent profit earned for the given years

= 1/6 x [40 + 55 + 45 + 65 + 70 + 60] = 335/6 = 55 5 .
6
6. During which of the following year was the ratio of income to the expenditure the minimum?
A. 1996
B. 1997
C. 1998
D. 1999

Answer: Option B

Explanation:

It is given that : % Profit = (Income – Expenditure)/Expenditure x 100
=> % Profit/100 = Income/Expenditure – 1
=> Income/Expenditure = % Profit/100 + 1.

From this it is clear that the ratio of income to expenditure is minimum for the year in which the % Profit has the minimum value. Since, out of given years (i.e., out of 1996, 1997, 1998, 1999 and 2000), the Company has the minimum % profit in the year 1997.

So the minimum ratio of income to expenditure is in the year 1997.

7. During which year the ratio of percentage profit earned to that in the previous year is the minimum?
A. 1996
B. 1997
C. 1998
D. 1999

Answer: Option B

Explanation:

The ratio percentage profit earned to that in the previous year, for different years are:

For 1996 = 55/40 = 1.38;
For 1997 = 45/55 = 0.82;
For 1998 = 65/45 = 1.44;
For 1999 = 70/65 = 1.08;
For 2000 = 60/70 = 0.86;

Clearly, this ratio is minimum for 1997.

8. If the expenditure in 2000 is 25% more than expenditure in 1997, then the income in 1997 is what percent less than the income in 2000?
A. 22.5%
B. 25%
C. 27.5%
D. 31.25%

Answer: Option C

Explanation:

Let the expenditure is 1997 be x.

Then, expenditure in 2000 = x + (25% of x) = 5/4 x.

Also, let the incomes in 1997 and 2000 be I1 and I2 respectively.

Then, for the year 1997, we have:

45 = (I1x)/x x 100     => 45/100 = I1 -1    =>     I1 = 145x/100 = 1.45x.
x

Also, for year 2000, we have:

60 =
( I2 5x/4 )
x 100     => 60/100 = 4I2

/5x

– 1     =>     I2 = 160/100 x 5x/4 = 2x.
( 5x/4 )

Difference between the two income = (2x – 1.45x) = 0.55x.

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