Rehmat’s marks in Maths are as follows: 60% in internal tests, 64% in the project, 73% in the final exam. The annual percentage score is calculated by combining the internals, project, and final exam in the ratio 3 : 2 : 5. What is Rehmat’s annual score in Maths?
Step-by-step solution
To find: Rehmat’s annual percentage score
Idea: The ratio 3 : 2 : 5 says how much each assessment counts. It is like listing 60 three times, 64 twice and 73 five times and taking the ordinary mean of these 10 numbers: a weighted mean.
- With weights 3, 2, 5 the data is the same as 60, 60, 60, 64, 64, 73, 73, 73, 73, 73 (ten values).½ mark
- Weighted sum = 60 × 3 + 64 × 2 + 73 × 5 = 180 + 128 + 365 = 673.1 mark
- Sum of weights = 3 + 2 + 5 = 10. Annual score = 67310 = 67.3%.1 mark
- Compare: with equal weightage it would be 60 + 64 + 733 ≈ 65.67%. The weighted score is higher because the final exam, her best score, carries the most weight (5 out of 10).½ mark
Check: Mean of the ten listed values: (180 + 128 + 365) ÷ 10 = 67.3 ✓. 67.3 lies between 60 and 73 and nearer 73, the most heavily weighted score ✓.
Answer to write in the exam
Annual score = 60 × 3 + 64 × 2 + 73 × 53 + 2 + 5
= 180 + 128 + 36510 = 67310
∴ Rehmat’s annual score = 67.3%
Common mistakes that cost marks
- Taking the plain average 65.67% and ignoring the ratio 3 : 2 : 5.
- Dividing by 3 (the number of assessments) instead of 10 (the sum of the weights).
- Matching the weights to the wrong scores, for example 60 × 5.
How this can come in the exam
A student scores 70% in a test and 80% in a project. They are combined in the ratio 1 : 3. The final score is
- 75%
- 77.5%
- 72.5%
- 78%
Show answer
(B) 77.5%
70 × 1 + 80 × 34 = 3104 = 77.5%.
In a speech contest, a speaker scores 8 for content, 6 for delivery and 9 for time-keeping. The weights are 5 : 3 : 2. Find the weighted score.
Show answer
8 × 5 + 6 × 3 + 9 × 25 + 3 + 2 (1 mark) = 40 + 18 + 1810 = 7.6 (1 mark).Try one yourself
A student scores 50% in internals, 70% in the project and 80% in the final exam, combined in the ratio 2 : 3 : 5. Find the annual score.
Show answer
50 × 2 + 70 × 3 + 80 × 510 = 100 + 210 + 40010 = 71%.
More questions like this
- Savitri’s marks in Kashmiri are as follows: 35 out of 50 in internal tests, 44 out of 60 in the project, and 80 out of 100 in the final exam. The annual percentage score is calculated by combining the internals, project, and final exam in the ratio 3 : 4 : 5. Which of the following expression(s) gives her annual score (as a percentage) in Kashmiri?
(i) 35 × 3 + 44 × 4 + 80 × 53 + 4 + 5
(ii) (35/100) × 3 + (44/100) × 4 + (80/100) × 53 + 4 + 5
(iii) (35/50) × 3 + (44/60) × 4 + (80/100) × 53 + 4 + 5 × 100
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(i) Salt: 5%, Sugar: 8% (ii) Salt: 13%, Sugar: 3% (iii) Salt: 6%, Sugar: 6%
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