Chapter 3 Proportional Reasoning-2 (Class 8 - Latest Maths NCERT (Ganita Prakash II) Solutions)
Need help with Chapter 3: Proportional Reasoning-2? You’ve come to the right place! This page provides comprehensive NCERT Solutions for the latest Class 8 Maths curriculum, helping you navigate complex, multi-variable systems with ease. We provide clear, step-by-step guidance on Ratios in Maps, explaining how to use a Representative Fraction (RF) to accurately calculate ground distances from a small sketch or map.
Our solutions offer detailed walkthroughs for Ratios with More than 2 Terms, ensuring you understand how to scale ingredients or construction materials proportionally. We also master the logic of "A Slice of the Pie"—providing precise methods for constructing Pie Charts. You will learn the mathematical logic of dividing $360^\circ$ into proportional sectors to visualize data, from student grades to seasonal trends, with perfect accuracy.
The final section of our solutions tackles Inverse Proportions, breaking down the constant relationship ($xy = k$) behind why more workers decrease work time or higher speeds shorten travel distances. These resources, meticulously curated by learningspot.co based on the Ganita Prakash II textbook, are designed to turn abstract proportionality into intuitive tools for data analysis and real-world problem-solving.
| Content On This Page | ||
|---|---|---|
| Figure It Out (Page No. 60) | Figure It Out (Page No. 62 - 63) | Figure It Out (Page No. 65) |
| Figure It Out (Page No. 67 - 68) | ||
Figure It Out (Page No. 60)
Question 1. A cricket coach schedules practice sessions that include different activities in a specific ratio — time for warm-up/cool-down : time for batting : time for bowling : time for fielding :: $3 : 4 : 3 : 5$. If each session is $150$ minutes long, how much time is spent on each activity?
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Question 2. A school library has books in different languages in the following ratio — no. of Odiya books : no. of Hindi books : no. of English books :: $3 : 2 : 1$. If the library has $288$ Odiya books, how many Hindi and English books does it have?
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Question 3. I have $100$ coins in the ratio — no. of $\textsf{₹}10$ coins : no. of $\textsf{₹}5$ coins : no. of $\textsf{₹}2$ coins : no. of $\textsf{₹}1$ coins :: $4 : 3 : 2 : 1$. How much money do I have in coins?
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Question 4. Construct a triangle with sidelengths in the ratio $3 : 4 : 5$. Will all the triangles drawn with this ratio of sidelengths be congruent to each other? Why or why not?
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Question 5. Can you construct a triangle with sidelengths in the ratio $1 : 3 : 5$? Why or why not?
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Figure It Out (Page No. 62 - 63)
Question 1. A group of $360$ people were asked to vote for their favourite season from the three seasons — rainy, winter and summer. $90$ liked the summer season, $120$ liked the rainy season, and the rest liked the winter. Draw a pie chart to show this information.
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Question 2. Draw a pie chart based on the following information about viewers' favourite type of TV channel: Entertainment — $50\%$, Sports — $25\%$, News — $15\%$, Information — $10\%$.
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Question 3. Prepare a pie chart that shows the favourite subjects of the students in your class. You can collect the data of the number of students for each subject shown in the table (each student should choose only one subject). Then write these numbers in the table and construct a pie chart:
| Subject | Number of Students |
|---|---|
| Language | |
| Arts Education | |
| Vocational Education | |
| Social Science | |
| Physical Education | |
| Maths | |
| Science |
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Figure It Out (Page No. 65)
Question 1. Which of these are in inverse proportion?
(i)
| $x$ | $40$ | $80$ | $25$ | $16$ |
|---|---|---|---|---|
| $y$ | $20$ | $10$ | $32$ | $50$ |
(ii)
| $x$ | $40$ | $80$ | $25$ | $16$ |
|---|---|---|---|---|
| $y$ | $20$ | $10$ | $12.5$ | $8$ |
(iii)
| $x$ | $30$ | $90$ | $150$ | $10$ |
|---|---|---|---|---|
| $y$ | $15$ | $5$ | $3$ | $45$ |
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Question 2. Fill in the empty cells if $x$ and $y$ are in inverse proportion.
| $x$ | $16$ | $12$ | $36$ | |
|---|---|---|---|---|
| $y$ | $9$ | $48$ |
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Figure It Out (Page No. 67 - 68)
Question 1. Which of the following pairs of quantities are in inverse proportion?
(i) The number of taps filling a water tank and the time taken to fill it.
(ii) The number of painters hired and the days needed to paint a wall of fixed size.
(iii) The distance a car can travel and the amount of petrol in the tank.
(iv) The speed of a cyclist and the time taken to cover a fixed route.
(v) The length of cloth bought and the price paid at a fixed rate per metre.
(vi) The number of pages in a book and the time required to read it at a fixed reading speed.
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Question 2. If $24$ pencils cost $\textsf{₹}120$, how much will $20$ such pencils cost?
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Question 3. A tank on a building has enough water to supply $20$ families living there for $6$ days. If $10$ more families move in there, how long will the water last? What assumptions do you need to make to work out this problem?
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Question 4. Fill in the average number of hours each living being sleeps in a day by looking at the charts. Select the appropriate hours from this list : $15, 2.5, 20, 8, 3.5, 13, 10.5, 18$.
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Question 5. The pie chart on the right shows the result of a survey carried out to find the modes of transport used by children to go to school. Study the pie chart and answer the following questions.
(i) What is the most common mode of transport?
(ii) What fraction of children travel by car?
(iii) If $18$ children travel by car, how many children took part in the survey? How many children use taxis to travel to school?
(iv) By which two modes of transport are equal numbers of children travelling?
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Question 6. Three workers can paint a fence in $4$ days. If one more worker joins the team, how many days will it take them to finish the work? What are the assumptions you need to make?
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Question 7. It takes $6$ hours to fill $2$ tanks of the same size with a pump. How long will it take to fill $5$ such tanks with the same pump?
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Question 8. A given set of chairs are arranged in $25$ rows, with $12$ chairs in each row. If the chairs are rearranged with $20$ chairs in each row, how many rows does this new arrangement have?
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Question 9. A school has $8$ periods a day, each of $45$ minutes duration. How long is each period, if the school has $9$ periods a day, assuming that the number of school hours per day stays the same?
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Question 10. A small pump can fill a tank in $3$ hours, while a large pump can fill the same tank in $2$ hours. If both pumps are used together, how long will the tank take to fill?
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Question 11. A factory requires $42$ machines to produce a given number of toys in $63$ days. How many machines are required to produce the same number of toys in $54$ days?
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Question 12. A car takes $2$ hours to reach a destination, travelling at a speed of $60$ km/h. How long will the car take if it travels at a speed of $80$ km/h?
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