Let's solve the given problem step-by-step.
1. Understanding the Relationship:
- We are given that Abha gets twice the marks as that of Palak.
- If Palak gets [tex]\( x \)[/tex] marks, then Abha gets [tex]\( 2x \)[/tex] marks.
Thus, we can express Abha's marks in terms of Palak's marks: Abha's marks = [tex]\( 2x \)[/tex].
2. Formulating the Equation:
- We are given another condition: two times Abha's marks and three times Palak's marks together make 280.
- Abha's marks are [tex]\( 2x \)[/tex], so two times Abha's marks would be [tex]\( 2 \times (2x) = 4x \)[/tex].
- Palak's marks are [tex]\( x \)[/tex], so three times Palak's marks would be [tex]\( 3x \)[/tex].
- According to the problem, these together make 280:
[tex]\[
4x + 3x = 280
\][/tex]
3. Solving the Equation for [tex]\( x \)[/tex]:
- Combining the terms on the left-hand side:
[tex]\[
4x + 3x = 7x
\][/tex]
- So the equation becomes:
[tex]\[
7x = 280
\][/tex]
- To find [tex]\( x \)[/tex], we divide both sides of the equation by 7:
[tex]\[
x = \frac{280}{7}
\][/tex]
- Calculating the division:
[tex]\[
x = 40
\][/tex]
Therefore, Palak gets [tex]\( 40 \)[/tex] marks.
4. Finding Abha's Marks:
- Since Abha's marks are twice that of Palak's marks:
[tex]\[
\text{Abha's marks} = 2x = 2 \times 40 = 80
\][/tex]
Therefore, Abha gets [tex]\( 80 \)[/tex] marks.
Summary:
- Marks obtained by Palak are [tex]\( 40 \)[/tex].
- Marks obtained by Abha are [tex]\( 80 \)[/tex].
