Data Interpretation Questions and Answers

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.

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.

Average percent profit earned for the given years

= 1/6 x [40 + 55 + 45 + 65 + 70 + 60] = 335/6 = 55(5/6)

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.

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.

Let the expenditure is 1998 be Rs. x crores.

Then, 65 = ((264 - x)/x) x 100  

=>  65/100 = (264/x) - 1

=> x = (264 x100)/165 = 160.

Therefore Expenditure in 1998 = Rs. 160 crores.

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 = (I₁ - x)/x x 100   =>   55/100 = I₁/x - 1  =>  I₁ = 155x/100 ... (i)

70 = (I₂ - x)/x x 100   =>   70/100 = I₂/x - 1 => I₂ = 170x/100 ... (ii)

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

I₁/I₂ = (155x/100)/(170x/100) = 155/170 ≈ 0.91/1 ≈ 9 : 10

The number of candidates qualified in 1999 = (80% of 26500) = 21200.

Therefore Number of candidates qualified in 2000 = (33500 - 21200) = 12300.

Let the number of candidates appeared in 2000 be x.

Then, 60% of x = 12300   =>  x = ( (12300 x 100)/60 ) = 20500

The total number of candidates who qualified in 1996 and 1997 together, cannot be determined until we know at least, the number of candidates who appeared in any one of the two years 1996 or 1997 or the percentage of candidates who qualified to candidates who appeared in 1996 and 1997 together.

Hence, the data is inadequate.

The number of candidates appeared in 1998 be x.

Then, 80% of x = 21200   =>   x = (21200 x 100)/80 = 26500 (required number)