In an examination, there were two papers, A and B, and the maximum mark in each of the two papers was 10. However, the weights assigned to papers A and B were in the ratio 2: 1, respectively. Jonathan scored 8 out of 10 in Paper A and an overall 70% in the examination. How much did he score in Paper B out of 10?

Let the score of Jonathan in Paper B be x out of 10.
The maximum mark for each paper is 10.

The weights for Paper A and Paper B are in the ratio 2:1.
We can treat this as a weighted average problem where:

Score in Paper A (X
A
​
) = 8

Weight of Paper A (W
A
​
) = 2

Score in Paper B (X
B
​
) = x

Weight of Paper B (W
B
​
) = 1

The overall percentage score is 70%. Out of a maximum of 10 scaled points, an overall 70% corresponds to a weighted average score of 7.

Using the weighted average formula:

Weighted Average=
W
A
​
+W
B
​

(X
A
​
×W
A
​
)+(X
B
​
×W
B
​
)
​

7=
2+1
(8×2)+(x×1)
​

7=
3
16+x
​

7×3=16+x
21=16+x
x=21−16=5
Jonathan scored 5 out of 10 in Paper B.