Two students appeared for an examination. One of them secured 21 marks more than the other and his marks were 80% of the sum of their marks. The marks obtained by them are:
- A88 and 67
- B89 and 68
- C28 and 7
- D98 and 77
Solution & Step-by-step Explanation
Let the marks obtained by the two students be x and y, where x>y.
According to the first condition:
x−y=21— (Equation 1)
According to the second condition, x is 80% of the sum of their marks:
x=
100
80
(x+y)
x=
5
4
(x+y)
5x=4x+4y
x=4y— (Equation 2)
Substitute the value of x from Equation 2 into Equation 1:
4y−y=21
3y=21
y=7
Now, substitute y=7 back into Equation 2:
x=4×7=28
Thus, the marks obtained by them are 28 and 7.
According to the first condition:
x−y=21— (Equation 1)
According to the second condition, x is 80% of the sum of their marks:
x=
100
80
(x+y)
x=
5
4
(x+y)
5x=4x+4y
x=4y— (Equation 2)
Substitute the value of x from Equation 2 into Equation 1:
4y−y=21
3y=21
y=7
Now, substitute y=7 back into Equation 2:
x=4×7=28
Thus, the marks obtained by them are 28 and 7.