Ncert Solution Class 9 Maths Ganita Manjari Exercise 10.2
chapter name
Learning Outcome: By the end of this chapter, students will be able to calculate weighted averages, solve mixture problems, interpret different types of charts, and make informed conclusions from data.
Question 1
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)
\[ \frac{35\times3+44\times4+80\times5}{3+4+5} \](ii)
\[ \frac{ \left(\frac{35}{100}\right)\times3+ \left(\frac{44}{100}\right)\times4+ \left(\frac{80}{100}\right)\times5 }{3+4+5} \](iii)
\[ \frac{ \left(\frac{35}{50}\right)\times3+ \left(\frac{44}{60}\right)\times4+ \left(\frac{80}{100}\right)\times5 }{3+4+5} \times100 \](iv)
\[ \frac{ \left(\frac{35}{50}\times100\right)\times3+ \left(\frac{44}{60}\times100\right)\times4+ \left(\frac{80}{100}\times100\right)\times5 }{3+4+5} \]Solution
Given:
Internal test marks = 35 out of 50
Project marks = 44 out of 60
Final exam marks = 80 out of 100
The ratio of internal test, project, and final exam is \(3:4:5\).
Step 1: Convert the marks into percentages.
\[ \text{Internal Test Percentage} =\frac{35}{50}\times100=70\% \] \[ \text{Project Percentage} =\frac{44}{60}\times100 =\frac{220}{3}\% \] \[ \text{Final Exam Percentage} =\frac{80}{100}\times100=80\% \]Step 2: Calculate the weighted average.
\[ \text{Annual Percentage} = \frac{ 70\times3+ \left(\frac{44}{60}\times100\right)\times4+ 80\times5 }{3+4+5} \] \[ = \frac{ 210+\frac{880}{3}+400 }{12} \] \[ = \frac{\frac{2710}{3}}{12} \] \[ =\frac{2710}{36} \]Checking the given expressions:
Expression (i) is incorrect because it uses raw marks without converting them to percentages.
Expression (ii) is incorrect because it divides all marks by 100 instead of using the maximum marks obtained in each component.
Expression (iii) is correct because it converts each component into a fraction of its maximum marks and then multiplies by 100.
Expression (iv) is correct because it first converts each component into a percentage and then calculates the weighted average.