In an examination the marks of Anil was 28.57% less than that of Barun’s marks and Barun’s marks was 11.11% less than that of Chandan’s marks. If the difference between the marks obtained by Anil and Chandan is 80.5 then find the marks obtained by Barun?

Solution

Let’s denote the marks obtained by Anil, Barun, and Chandan as \(A\), \(B\), and \(C\) respectively.

Given:
– Anil’s marks are 28.57% less than Barun’s marks: \(A = B – 0.2857B = 0.7143B\).
– Barun’s marks are 11.11% less than Chandan’s marks: \(B = C – 0.1111C = 0.8889C\).
– The difference between the marks obtained by Anil and Chandan is 80.5: \(C – A = 80.5\).

Step 1: Express Anil’s marks in terms of Chandan’s marks

Using the relation between Anil’s and Barun’s marks:
\[ A = 0.7143B \]
Using the relation between Barun’s and Chandan’s marks:
\[ B = 0.8889C \]

So, Anil’s marks in terms of Chandan’s marks:
\[ A = 0.7143 \times 0.8889C = 0.6351C \]

Step 2: Use the difference between Anil’s and Chandan’s marks

\[ C – A = 80.5 \]
\[ C – 0.6351C = 80.5 \]
\[ 0.3649C = 80.5 \]
\[ C = \frac{80.5}{0.3649} \]
\[ C = 220.5 \]

Step 3: Find Barun’s marks

Using the relation between Barun’s and Chandan’s marks:
\[ B = 0.8889C \]
\[ B = 0.8889 \times 220.5 \]
\[ B = 196 \]

Conclusion

The marks obtained by Barun are 196.