NCERT Solutions for Class 9 Maths Chapter 10 — Exercise Set 10.2#

When parts are combined in a ratio such as $3 : 4 : 5$, the ratio gives the weights. First turn each score into the same scale (a fraction or a percentage), then take the weighted mean.

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? #

$$\text{(i)}\ \dfrac{35 \times 3 + 44 \times 4 + 80 \times 5}{3 + 4 + 5} \qquad \text{(ii)}\ \dfrac{\frac{35}{100} \times 3 + \frac{44}{100} \times 4 + \frac{80}{100} \times 5}{3 + 4 + 5}$$

$$\text{(iii)}\ \dfrac{\frac{35}{50} \times 3 + \frac{44}{60} \times 4 + \frac{80}{100} \times 5}{3 + 4 + 5} \times 100 \qquad \text{(iv)}\ \dfrac{\left(\frac{35}{50} \times 100\right) \times 3 + \left(\frac{44}{60} \times 100\right) \times 4 + \left(\frac{80}{100} \times 100\right) \times 5}{3 + 4 + 5}$$
Solution

The three marks are out of different totals (50, 60, 100), so each must first be turned into a fraction or percentage of its own total:

$$\dfrac{35}{50} = 70\%, \quad \dfrac{44}{60} \approx 73.33\%, \quad \dfrac{80}{100} = 80\%$$
  • (i) Wrong. It uses the raw marks, which are out of different totals.
  • (ii) Wrong. It divides every mark by 100, but the internals and project are not out of 100.
  • (iii) Correct. Each mark is divided by its own total, the weighted mean is taken, and the result is changed into a percentage.
  • (iv) Correct. Each mark is first changed into a percentage, then the weighted mean is taken. This is the same as (iii).

∴ Expressions (iii) and (iv) give her annual score. Its value is:

$$\text{Score} = \dfrac{70 \times 3 + 73.33 \times 4 + 80 \times 5}{12}$$

$$\text{Score} = \dfrac{210 + 293.33 + 400}{12}$$

$$\text{Score} \approx 75.28\%$$

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