Two friends, Rama and Jaya, appeared an examination. Rama secured 8 marks more than Jaya and her marks was 55% of the sum of their marks. The marks obtained by them are:
Show Hint
- 38, 46
- 36, 44
- 41, 49
- 32, 40
The Correct Option is B
Solution and Explanation
We are given two conditions related to the marks of Rama and Jaya. We need to set up a system of linear equations and solve for their individual marks.
Step 2: Key Formula or Approach:
Let R be the marks obtained by Rama and J be the marks obtained by Jaya.
Translate the given English statements into mathematical equations.
1. "Rama secured 8 marks more than Jaya": \(R = J + 8\)
2. "her marks was 55% of the sum of their marks" (Here 'her' refers to Rama): \(R = \frac{55}{100}(R+J)\)
Solve these two equations simultaneously.
Step 3: Detailed Explanation:
We have the two equations:
(1) \(R = J + 8\)
(2) \(R = 0.55(R + J)\)
Substitute the value of R from equation (1) into equation (2):
\[ J + 8 = 0.55((J + 8) + J) \] \[ J + 8 = 0.55(2J + 8) \] Now, solve for J:
\[ J + 8 = 1.1J + 4.4 \] \[ 8 - 4.4 = 1.1J - J \] \[ 3.6 = 0.1J \] \[ J = \frac{3.6}{0.1} = 36 \] So, Jaya's marks are 36.
Now, find Rama's marks using equation (1):
\[ R = J + 8 = 36 + 8 = 44 \] So, Rama's marks are 44.
The marks obtained by them are 36 and 44.
Step 4: Final Answer:
The marks obtained by Jaya and Rama are 36 and 44, respectively. This corresponds to option (B).
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Questions Asked in SRCC GBO exam
Read the given passage and answer the questions.
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