Two students appeared for an examination. One student who scored 20 marks more than the other, his score was 60% of the sum of their marks. What was his score?
- A80
- B20
- C40
- D60
Solution & Step-by-step Explanation
Let the marks obtained by the two students be x and y, where x is the higher score.
According to the first condition:
x=y+20⟹y=x−20
According to the second condition:
x=60% of (x+y)
x=
100
60
(x+y)
x=
5
3
(x+y)
5x=3x+3y
2x=3y
Substitute the value of y=x−20 into this equation:
2x=3(x−20)
2x=3x−60
3x−2x=60
x=60
Thus, the higher score (his score) is 60.
According to the first condition:
x=y+20⟹y=x−20
According to the second condition:
x=60% of (x+y)
x=
100
60
(x+y)
x=
5
3
(x+y)
5x=3x+3y
2x=3y
Substitute the value of y=x−20 into this equation:
2x=3(x−20)
2x=3x−60
3x−2x=60
x=60
Thus, the higher score (his score) is 60.