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 marks secured by C in Hindi were 33⅓% higher than D’s Mathematics marks, while C’s English marks were 10 greater than E’s Mathematics marks. If C obtained 275 marks altogether in the three subjects, determine A’s Mathematics marks.

The correct answer is 112.5.

Step 1: Understand the distribution from the pie chart
From the given pie chart, the percentage distribution of total marks obtained in Mathematics by five students (A, B, C, D, and E) is as follows:
• A = 12.5%
• B = 30.5%
• C = 14%
• D = 18%
• E = 15%

Let the total marks obtained by all five students in Mathematics combined be $M$.

Therefore, the Mathematics marks of the students in terms of $M$ are:
• Mathematics marks of C = 14% of $M$ = $\frac{14M}{100}=0.14M$
• Mathematics marks of D = 18% of $M$ = $\frac{18M}{100}=0.18M$
• Mathematics marks of E = 15% of $M$ = $\frac{15M}{100}=0.15M$
• Mathematics marks of A = 12.5% of $M$ = $\frac{12.5M}{100}=0.125M$

Step 2: Express C's marks in Hindi and English
According to the problem statement:
1. C's marks in Hindi were 33¹/₃% (which is equal to ¹/₃) higher than D's Mathematics marks:

$\text{C’s Hindi Marks}=\text{D’s Math Marks}+\frac{1}{3}\times \text{D’s Math Marks}=\frac{4}{3}\times \left(0.18M\right)=0.24M$

2. C's marks in English were 10 greater than E's Mathematics marks:

$\text{C’s English Marks}=\text{E’s Math Marks}+10=0.15M+10$

Step 3: Calculate the total Mathematics marks ($M$)
The total marks obtained by C in all three subjects (Hindi, English, and Mathematics) is 275:

$\text{C’s Total Marks}=\text{C’s Hindi Marks}+\text{C’s English Marks}+\text{C’s Math Marks}$

$275=0.24M+(0.15M+10)+0.14M$

$275=0.53M+10$

$0.53M=275-10=265$

$M=\frac{265}{0.53}=500$

Step 4: Calculate A's Mathematics marks
Now that we have the total Mathematics marks $M=500$, we can determine A's Mathematics marks:

$\text{A’s Mathematics Marks}=12.5\%\text{of}500=0.125\times 500=112.5$

Thus, A’s Mathematics marks are 112.5.