Question

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:

• A. 38, 46
• B. 36, 44
• C. 41, 49
• D. 32, 40

Hint:

For word problems, accurately translating the statements into equations is the most crucial step. Double-check the pronouns like 'her' to ensure you're assigning the relationship to the correct person.

Answer 1

The Correct Option is B

Strategy:

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.

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.

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.

The marks obtained by Jaya and Rama are 36 and 44, respectively. This corresponds to option (B).