Class 9 Maths Ganita Manjari Ch 10 Exercise 10.2 Solutions

How to solve every question

annual score % = p₁w₁ + p₂w₂ + p₃w₃w₁ + w₂ + w₃

Make every mark a percentage Divide each mark by its own maximum and multiply by 100, so all parts are on the same scale.

Attach the weights The ratio 3 : 4 : 5 gives the weights. Multiply each percentage by its weight.

Add and divide Divide the total by the sum of the weights, 3 + 4 + 5 = 12.

Test each option An expression is correct only if it gives the same answer as this method.

Percentage (p): a mark expressed out of 100, such as 35 out of 50 = 70%.

Weight (w): how much a part counts, here 3, 4 and 5 for internals, project and final exam.

Common mistake: weighting raw marks that are out of different totals.

Custom weights

Question 1: Savitri's annual score in Kashmiri

Answer: (iii) and (iv)

Question: Savitri scored 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 is found by combining these in the ratio 3 : 4 : 5. Which of the expressions (i) to (iv) gives her annual score as a percentage?

Step 1 · Write each mark as a percentage

Part	Marks	Percentage	Weight
Internal tests	35 out of 50	70%	3
Project	44 out of 60	73.33%	4
Final exam	80 out of 100	80%	5

The three parts have different maximum marks (50, 60 and 100), so we cannot weight the raw marks directly.

Step 2 · Find the correct annual score

70 × 3 + 73.33 × 4 + 80 × 53 + 4 + 5 = 210 + 293.33 + 40012 = 903.3312 ≈ 75.28%

Q1 · the heaviest weight is on the final exam (80%), which pulls the score above the simple average of 74.4%

Step 3 · Test option (i)Not correct

35 × 3 + 44 × 4 + 80 × 53 + 4 + 5 = 105 + 176 + 40012 = 68112 = 56.75

This weights the raw marks, which are out of 50, 60 and 100. The result is not a percentage and does not match 75.28.

Step 4 · Test option (ii)Not correct

Option (ii) divides each mark by 100, as if every part were out of 100. So it uses 0.35, 0.44 and 0.80 instead of 0.70, 0.733 and 0.80.

0.35 × 3 + 0.44 × 4 + 0.80 × 512 = 1.05 + 1.76 + 412 = 6.8112 = 0.5675

That is 56.75%, which is wrong for the same reason as (i).

Step 5 · Test option (iii)Correct

Here each mark is divided by its own maximum: 3550 = 0.70, 4460 ≈ 0.7333 and 80100 = 0.80. The whole fraction is then multiplied by 100.

0.70 × 3 + 0.7333 × 4 + 0.80 × 512 × 100 = 9.033312 × 100 ≈ 75.28%

Step 6 · Test option (iv)Correct

Here each fraction is multiplied by 100 first, so the parts become 70, 73.33 and 80. This is exactly the calculation in Step 2.

70 × 3 + 73.33 × 4 + 80 × 512 ≈ 75.28%

Options (iii) and (iv) give Savitri's annual score, about 75.28%. Options (i) and (ii) are wrong because they ignore that the three parts have different maximum marks.

Answer at a glance

Convert each mark to a percentage first, then apply the weights 3, 4 and 5.

Question	What is asked	Weights used	Answer
Q1	Which expressions give the annual score	Internals 3, project 4, final 5	(iii) and (iv), both ≈ 75.28%

Source of the questions: NCERT, Ganita Manjari, Grade 9, Part II, Chapter 10, Exercise 10.2. The solutions, explanations and diagrams on this page are our own working.