Class 9 Maths Ganita Manjari Ch 10 Exercise 10.5 Solutions

How to draw a 100% stacked bar

share of a part = parttotal × 100

Find each total Add the parts in each row. Here every person has 24 hours.

Find each share Divide each part by its row total and multiply by 100.

Check The shares of every row should add up to 100%.

Draw Make every bar the same length, 0% to 100%, and place the segments one after another.

100% stacked bar: a stacked bar scaled to a fixed length, so it shows shares and not amounts.

Share: the part of the whole, written as a percentage.

What it hides: two bars of the same length can stand for very different totals.

A 100% stacked bar of body-states

Question 1: Smart watch data of 5 people

Answer: Sahana 8-8-8, Julie desk job

Question: Smart watches tracked the average hours per day (Monday to Friday) that 5 people spent lying down, sitting, and standing or moving around. (i) Guess Sahana's row. (ii) Guess what work Julie might do. (iii) Complete the 100% stacked bar chart.

Step 1 · Every row adds up to 24 hours

	Lying down	Sitting	Standing / moving	Total
Pavani (Patient)	20	3	1	24
Raghu (Nurse)	7	4	13	24
Zakir (Teacher)	8	6	10	24
Sahana (Student)				24
Julie (?)	8	10	6	24

A day has 24 hours, so each person's three numbers must add up to 24. We use this to check Sahana's guess.

Part (i) · Guess Sahana's row

This is a guess, so many answers are reasonable. A student sleeps about 8 hours, sits for about 8 hours in class, at the desk and on a phone or computer, and is on their feet or moving around for the rest.

	Lying down	Sitting	Standing / moving	Total
Sahana (Student)	8	8	8	24

Check: 8 + 8 + 8 = 24. Any other split that adds up to 24 and is close to this is also fine, for example 8, 9, 7.

Part (ii) · Guess Julie's work

Julie lies down 8 hours (sleep), sits for 10 hours, and is on her feet or moving only 6 hours. The long sitting time points to a desk job or a job where one sits all day.

Good guesses: a software engineer, an accountant, a bank clerk or a driver. Compare with Raghu, a nurse, who is on his feet for 13 hours. Your classmates may guess differently, and that is fine because the data does not name a job.

Part (iii) · Turn each row into percentages

In a 100% stacked bar, each person's 24 hours becomes 100%. Each part is hours24 × 100.

Pavani: 2024 × 100 ≈ 83.3%, 324 × 100 = 12.5%, 124 × 100 ≈ 4.2%

Raghu: 724 × 100 ≈ 29.2%, 424 × 100 ≈ 16.7%, 1324 × 100 ≈ 54.2%

Zakir: 824 × 100 ≈ 33.3%, 624 × 100 = 25%, 1024 × 100 ≈ 41.7%

Julie: 824 × 100 ≈ 33.3%, 1024 × 100 ≈ 41.7%, 624 × 100 = 25%

	Lying down	Sitting	Standing / moving
Pavani (Patient)	83.3%	12.5%	4.2%
Raghu (Nurse)	29.2%	16.7%	54.2%
Zakir (Teacher)	33.3%	25.0%	41.7%
Sahana (Student)	33.3%	33.3%	33.3%
Julie (Office worker)	33.3%	41.7%	25.0%

Draw each bar from 0% to 100%, with the segments one after another: lying down first, then sitting, then standing or moving. Every bar has the same total length, 100%.

Q1 · all five bars have the same length, so we compare shares, not hours

What the chart shows: Pavani is mostly lying down, which fits a patient. Raghu is mostly on his feet, which fits a nurse. Julie spends the largest share sitting. The bars match the jobs, which is why this chart is useful.

(i) Sahana: 8, 8, 8 hours (a reasonable guess). (ii) Julie most likely has a desk or sitting job. (iii) The completed 100% stacked bars are drawn above, with every bar adding up to 100%.

Answer at a glance

Turn every row into percentages that add to 100%, then draw bars of equal length.

Question	What is asked	What we use	Answer
Q1	Guess Sahana, guess Julie, draw the chart	Row totals of 24 hours	Sahana 8, 8, 8; Julie has a desk job; bars drawn

Source of the questions: NCERT, Ganita Manjari, Grade 9, Part II, Chapter 10, Exercise 10.5. The solutions, explanations and diagrams on this page are our own working.