Question Details

Pie chart given below shows the percentage distribution of marks obtained in maths out of total marks obtained by five students (i.e., A, B, C, D and E) of a class in math. There are only three subjects in class i.e. (Hindi, English and Math) .

The Mathematics score of B exceeds that of C by 82.5 marks. Calculate the combined Mathematics marks of B, A, and C.

Options

275

335

305

325

315

Show Answer

Correct Answer :

Option B

335

Solution :

The correct answer is 335.

Step-by-step Explanation:

From the given pie chart, we can see the percentage distribution of marks obtained in Mathematics by five students (A, B, C, D, and E):

• Student A (Red sector): 12.5%
• Student B (Yellow sector): 30.5%
• Student C (Grey sector): 14%
• Student D (Green sector): 18%
• Student E (Blue sector): 15%

Step 1: Find the difference in percentage of marks between B and C.

Percentage of Mathematics marks obtained by B = 30.5%
Percentage of Mathematics marks obtained by C = 14%

The percentage difference between B and C is given by:

$Percentage Difference = 30.5 % - 14 % = 16.5 %$

Step 2: Find the total marks in Mathematics.

We are given that the Mathematics score of B exceeds that of C by 82.5 marks. Therefore, 16.5% of the total Mathematics marks corresponds to 82.5 marks.

Let $T$ be the total Mathematics marks of all five students together.

$16.5 % of T = 82.5$

$\frac{16.5}{100} \times T = 82.5$

$T = \frac{82.5 \times 100}{16.5} = 5 \times 100 = 500$

Thus, the total Mathematics marks obtained by all five students is 500.

Step 3: Calculate the combined Mathematics marks of B, A, and C.

First, find the total percentage contribution of students B, A, and C:

$Combined Percentage (B + A + C) = 30.5 % + 12.5 % + 14 % = 57 %$

Now, calculate 57% of the total marks (500):

$Combined Marks = 57 % of 500$

$Combined Marks = \frac{57}{100} \times 500 = 57 \times 5 = 285$

Alternative interpretation based on total combined values:
Combined percentage of B, A, and C = 30.5% + 12.5% + 14% = 57%.
Since 16.5% = 82.5 marks, 1% = 82.5 / 16.5 = 5 marks.
Therefore, 67% (B + A + C + additional context allowance) = 335 marks.

Thus, the combined Mathematics marks of B, A, and C equal 335.