Mr. Madan got 9 out of 10 marks in English, 15 out of 16 in life sciences and the ratio of the percentage of his marks in English and Mathematics is 15: 16. If the total marks of Mathematics are 20, then find the difference of the percentage of his marks in Mathematics and life sciences.

The correct answer is 2.25%.

Let us solve the problem step-by-step by calculating the percentage of marks Mr. Madan obtained in each subject.

Step 1: Calculate the percentage of marks in English
Mr. Madan got 9 out of 10 marks in English.
Percentage in English = $(\frac{9}{10}\times 100)\%=90\%$

Step 2: Calculate the percentage of marks in Life Sciences
He got 15 out of 16 marks in Life Sciences.
Percentage in Life Sciences = $(\frac{15}{16}\times 100)\%=\frac{375}{4}\%=93.75\%$

Step 3: Calculate the percentage of marks in Mathematics
We are given that the ratio of the percentage of marks in English to Mathematics is 15 : 16.
Let the percentage of marks in Mathematics be M%.
Using the given ratio:
$\frac{\text{English \%}}{\text{Mathematics \%}}=\frac{15}{16}$
$\frac{90}{M}=\frac{15}{16}$
Solving for M:
$M=\frac{90\times 16}{15}=6\times 16=96\%$
So, the percentage of marks in Mathematics is 96%.

Step 4: Find the difference between the percentage of marks in Mathematics and Life Sciences
Difference = Percentage in Mathematics - Percentage in Life Sciences
$\text{Difference}=96\%-93.75\%=2.25\%$

Thus, the difference between the percentage of his marks in Mathematics and Life Sciences is 2.25%.