RS Aggarwal solution class 8 chapter 23 Line Graphs and Linear Graphs Exercise 23

Exercise 23

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Q1 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 1:

The following table depicts the maximum temperature on the seven days of a particular week. Study the table and draw a line graph for the same.

Day	Sun	Mon	Tues	Wed	Thurs	Fri	Sat
Maximum temp. (in °C)	25	28	26	32	29	24	31

Answer 1:

Q2 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 2:

Consider the following input/output table. Draw a line graph for it.

Input	1	2	4	5	7
Output	2	5	11	14	20

Now, use the graph drawn to predict the outputs for the inputs of 3 and 8.

Answer 2:

From the graph, we can see that out for the inputs of 3 and 8 are 8 and 23 respectively.

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Q3 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 3:

The table given below depicts the annual gross profit of a company for a period of 5 years. Study the table and draw a line graph for the same.

Year	2013	2014	2015	2016	2017
Gross profit (in lakhs of Rs)	17	15.5	11.4	12.1	14.9

Answer 3:

ans

Q4 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 4:

Ajeeta starts off from home at 7 a.m. with her father on a scooter that goes at a uniform speed of 30 km/hr. Her father drops her at her school after half an hour. She stays in the school till 1.30 p.m. and takes an autorickshaw to return home. The autorickshaw has a uniform speed of 10 km/hr. Draw the line graph for the given situation and also determine the distance of Ajeets's school from her home.

Answer 4:

distance of Ajeets's school from her home is given by
speed = $\frac{\mathrm{distance}}{\mathrm{time}}$
30 = $\frac{\mathrm{distance}}{1/2}$

distance = 15 km

Distance-Time graph is given by

Q5 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 5:

The following table shows the percentage of students who dropped out of school after completing high school.

Year	2005	2007	2009	2011	2013	2015	2017
Percentage of students who dropped out of school	6%	5.5%	5%	4.7%	4.9%	4%	4.5%

Study the above table carefully and draw a line graph to depict it.

Answer 5:

ans

Q6 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 6:

The following table shows the percentage of students who dropped out of school after completing high school

Age (in Year)	8	9	10	11	12	13	14	15	16	17	18
Boys	72%	75%	78%	81%	84%	88%	92%	95%	98%	99%	100%
Girls	77%	81%	84%	88%	91%	95%	98%	99%	99.5%	100%	100%

Now, use the graph to answer the following question:
(i)  In which year both boys and the girls achieve their maximum height?
(ii) Who grows faster at puberty (14 years to 16 years of age)

Answer 6:

(i) Both boys and girls achieve their maximum height in 18th years.
(ii) Boys grows faster than girls in puberty.

Q7 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 7:

A car is travelling from city P to city Q, which are 350 km apart. The line graph given below describes the distances of the car from the city P at different times.

Study the above graph and answer the questions given below:
(i)     What information is given on the two axes?

(ii)    From where and when did the car begin its journey?

(iii)   How far dis the car go in the first hour?

(iv)   How far did the car go during (a) the 2nd hour and (b) the 3rd hour?

(v)    Was the speed same during first three hours? How do you know it?

(vi)   Did the car stop for some during at any place? Justify your answer.

(vii)  When did the car reach city Q?

Answer 7:

(i) The x-axis shows the time y-axis shows the distance of the car from city P.
(ii) The car begins its journey from city P at 8:00 a.m.
(iii) The car covers 50km in first hour.
(iv) The car covers
       (a) 100 km in second hour.
       (b) 50km in third hour.

(v) No, because the distance covered per hour is not uniform.
(vi)  Yes, the car stopped during the interval 11 a.m. to 12 a.m. ,as indicated by horizontal line segment during this           period.
(vii) At 2 p.m ,the car reached at the city Q.

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Q8 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 8:

A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distances from the town at different times are shown by the given graph.

Study the above graph carefully and answer the questions given below:

(i)     What is the scale taken for the time-axis?

(ii)    How much time did the person take for the travel?

(iii)   How far is the place of the merchant from the town?

(iv)   Did the person stop on his way? Explain.

(v)    During which period did the ride fastest?

Answer 8:

(i) The scale taken at time-axis is 1 unit = 15 minutes.
(ii) The person travels for 3 hours 30 minutes.
(iii) The place of merchant is 22 km from the town.
(iv) Yes, the person stopped from 10 a.m. to 11 a.m. as indicated by the horizontal line in the graph.
(v) He ride fastest during 8 a.m. to 9 a.m.

Q9 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 9:

A man started his journey on his car from location a and came back. The graph given below shows his position at different times during the whole journey.

Study the above graph carefully and answer the questions given below:
(i)     At what time did he start and end his journey?

(ii)    What was the total duration of the journey?

(iii)   Which journey, onward or return, was of longer duration?

(iv)   For how many hours did he not move?

(v)    At what time did he have the fastest speed?

Answer 9:

(i) He starts his journey at 5.30 a.m. and end at 6 p.m.
(ii) Total duration of the journey was 12 hr 30 min.
(iii) Forward.
(iv) He did not move for 6 hours.
(v) He had the fastest speed from 2 p.m. to 5.30 p.m.

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Q10 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 10:

The line graph given below shows the yearly sales figures for a manufacturing company during the last five years.

Study the above graph carefully and answer the questions given below:
(i)     What were the sales in (a) 2013  (b) 2015  (c) 2016?

(ii)    Compute the difference between the sales in 2012 and 2016?

(iii)   In which year was there the greatest difference between the sales as compared to its previous year?

Answer 10:

(i) The sales in
  (a) 2013 was Rs 7 cr
  (b) 2015 was Rs10 cr
  (c) 2016 was Rs 8 cr
(ii) The difference between the sales in 2012 and 2016 is Rs 4 cr.
(iii) The greatest difference was in 2015.

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Q11 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 11:

The following is the distance-time graph of amit's walking.

Study the above graph carefully and answer the questions given below:
(i)     When does Amit make the least progress? Explain your answer.

(ii)    Find his average speed in km/hr.

Answer 11:

(i) Amit make least progress from 25 min to 40 min, as indicated by the line in the graph.
(ii) Total distance covered = 2km
      Total time = 55 min = $\frac{55}{60}$ hr
     Average speed = $\frac{\mathrm{Total} \mathrm{distance} \mathrm{covered} }{ \mathrm{Total} \mathrm{time}}$ = $\frac{2}{55}\times 60=2.18$ km/hr

Q12 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 12:

For an experiment in botany, two different plants, plant A and plant B, were grown under similar laboratory conditions. Their heights were measured at the end of each week for three weeks. The results are shown by the line graph given below:

Study the above graph carefully and answer the questions given below:
(i)     How high was plant A after (a) 2 weeks (b) 3 weeks?

(ii)    How high was plant B after (a) 2 weeks (b) 3 weeks?

(iii)   How much did plant A grow during the 3rd week?

(iv)   How much did plant B grow from the end of the 2nd week to the end of the 3rd week?

(v)    During which week did plant A grow most?

(vi)   During which week did plant B grow least?

(vii)  Were the two plants of the same height during any week shown here? Specify.

Answer 12:

(i) Plant A was
   (a) 7 cm high after 2 weeks.
   (b) 9 cm high after 3 weeks.

(ii) Plant B was
   (a) 7 cm high after 2 weeks.
   (b) 10 cm high after 3 weeks.
(iii) Plant A grow 2 cm during the 3rd week.
(iv) Plant B grow 3 cm in the given period.
(v) Plant A grow most in 2nd week.
(vi) Plant B grow least in 1st week.
(vii) At the end of the 2nd week both plants were of same height can be seen in the graph.

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Q13 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 13:

The following line graph shows the change in temperature of a block of ice when heated.

Study the above graph carefully and answer the questions given below:
(i)     For how many seconds did the ice block have no change in temperature?

(ii)    For how long was there a change in temperature?

(iii)   After how many seconds of heating did the temperature become constant at 100° C?

(iv)   What was the temperature after 25 seconds?

(v)    What will be the temperature after 1.5 minutes? Justify your answer.

Answer 13:

(i) The ice block had no change for 20 seconds.
(ii) There was a change in the temperature for 30 seconds
(iii) After 50 second, the temperature became constant at 100⁰ c.
(iv) The temperature after 25 second was 18⁰ c.
(v)  The temperature after 1.5 min will be 100⁰ c as it is uniform after 50 seconds.

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Q14 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 14:

The following line graph shows the temperature forecast and the actual temperature for each day of a week.

Study the above graph carefully and answer the questions given below:
(i)     On which days was the forecast temperature the same as the actual temperature?

(ii)    What was the maximum forecast temperature during the week?

(iii)   What was the minimum actual temperature during the week?

(iv)   On which day did the actual temperature differ the most from the forecast temperature?

Answer 14:

(i) On Tuesday, Friday, Sunday the forecast temperature was same as the actual temperature.
(ii) Maximum forecast temperature was 35⁰ c during the week.
(iii) Minimum actual temperature was 15⁰ c during the week.
(iv) On Thursday, the actual temperature differ the most from the forecast temperature.

Q15 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 15:

The following distance-time graph is for a car travelling to certain places.

Study the above graph carefully and answer the questions given below:
(i)     How far does the car travel in $4\frac{1}{2}$ hours?

(ii)    How much time does the car take to reach R?

(iii)   How long does the car take to cover 80 km?

(iv)   How far is Q from the starting point?

(v)    When does the car reach the place S after starting?

Answer 15:

(i) The car travels 180 km in $4\frac{1}{2}$ hours.
(ii) The car takes  5 hours to reach R.
(iii) The car takes 2 hours to cover 180 km.
(iv) Q is 120 km far from the starting point.
(v) The car reach the place S after 6 hours.

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Q16 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 16:

The following line graph shows the journey made by two cyclists, cyclist I and cyclist II, one from town B to town A and the other from town A to town B.

Study the above graph carefully and answer the questions given below:
(i)     At what time did cyclist II rest? For how long did the cyclist rest?

(ii)    Was cyclist II cycling faster or slower after the rest?

(iii)   At what time did the two cyclists meet?

(iv)   How far had cyclist II travelled when he met cyclist I?

(v)    When cyclist II reached town B, how far was cyclist I from town A?

Answer 16:

(i) Cyclist II rest at 8.45 a.m. for 15 min.
(ii) Cyclist II was faster after the rest.
(iii) The two cyclist met at 9 a.m.
(iv) Cyclist II travelled 10 km when he met cyclist I.
(v) Cyclic I was 10 km far from town A.

Q17 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 17:

The following table gives the distances travelled by a car at various time-intervals. Study the table and draw a linear graph for the same.

Time	6 a.m.	7 a.m.	8 a.m.	9 a.m.
Distance (in km)	40	80	120	160

From your graph, answer the questions given below:

(i)     How much distance did the car cover during the period from 7.30 a.m. to 8 a.m.

(ii)    What was the time when the car had covered a distance of 100 km, since its start?

(iii)   How much distance had the car covered by 8.30 a.m.?

Answer 17:

(i) The car covers 20 km during the period from 7.30 a.m. to 8 a.m.
(ii) The car covered 100 km at 7.30 a.m.
(iii) The car covered 140 km by 8.30 a.m.

Q18 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 18:

Study the table given below and draw a line graph for it.

Side of the square (in cm)	2	3	3.5	5	6
Perimeter (in cm)	8	12	14	20	24

Is the graph drawn, a linear graph?

Answer 18:

Yes, we can see that the drawn graph is linear.

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Q19 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 19:

Study the table given below and draw a line graph for it.

Side of the square (in cm)	2	3	4	5	6
Area (in cm2)	4	9	16	25	36

Is the graph drawn, a linear graph?

Answer 19:

No, the drawn graph is not linear.

Q20 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 20:

Plot a line graph for the variables p and q, where p is four times q, i.e., the equation is p = 4q.
Using the graph, find the value of (i) p, when q = 6 and (ii) q, when p = 20.

Answer 20:

We have p = 4q
(i) When q = 6
      then p = $4\times 4=16$
 (ii) when p = 20
       then,  20 = 4q
                 5 = q

And the graph of p = 4q is given by 

q	1	2	3	4	5	6
p	4	8	12	16	20	24

      

                                                                                                                                                                                                                                                                  

Q21 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 21:

Plot a line graph for the variables x and y , where y = 2x + 1.
Using the graph, find the value of (i) y, when x = 5 and (ii) x, when y = 13.

Answer 21:

We have the following table for y = 2x+1

x	0	1	2	3	4
y	1	3	5	7	9

Q22 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 22:

A bank gives 10% simple interest on deposits by senior citizens. Draw a line graph to illustrate the relation between the sum deposited and the simple interest earned.
Find from the graph:
(i)    The annual interest obtainable for a investment of Rs 250
(ii)   The investment one has to make in order to get an annual simple interest of Rs 70

Answer 22:

$$\begin{gathered} \mathrm{Using} SI=\frac{P\times R\times T}{100} \\ \mathrm{Where} \mathrm{SI}= \mathrm{simple} \mathrm{interest} \\ \mathrm{P}=\mathrm{principal} \\ \mathrm{R}= \mathrm{rate} \mathrm{of} \mathrm{interest} \\ \mathrm{T}=\mathrm{time} \end{gathered}$$

We have,

P	500	1000	1500	2000
SI	50	100	150	200

(i) Given sum deposited i.e P = 250 , R = 10%, Time = 1 year
using formula we have,

$$\begin{gathered} SI=\frac{250\times 10\times 1}{100} \\ SI=25 \mathrm{Rs} \end{gathered}$$

Hence, the annual interest for an investment of 250 rs is 25 rs.

(ii) Given annual simple interest = 70 rs , R = 10%, T=1 year
using formula we have,

$$\begin{gathered} 70=\frac{P\times 10\times 1}{100} \\ 700=P \\ \mathrm{Hence}, \mathrm{he} \mathrm{has} \mathrm{to} \mathrm{invest} 700 \mathrm{rs} \mathrm{in} \mathrm{order} \mathrm{to} \mathrm{get} \mathrm{an} \mathrm{annual} \mathrm{simple} \mathrm{interest} \mathrm{of} 70 \mathrm{rs} \end{gathered}$$

Q23 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 23:

Sajal can ride a scooter constantly at a speed of 30 km/hr. draw a distance-time graph for this situation.
Use the graph drawn to find:
(i)   The time taken by Sajal to ride 75 km
(ii)  The distance covered by Sajal in $3\frac{1}{2}$ hours

Answer 23:

We have,
speed $=\frac{\mathrm{distance}}{\mathrm{time}}$


We have the following table for Distance-Time graph
 

Time(hrs)	1	2	3	4
Distance(km)	30	60	90	120

(i) Given speed = 30 km/hr , distance = 75 km
using formula we have
$$\begin{gathered} 30=\frac{75}{\mathrm{time} \mathrm{taken }} \\ \mathrm{time} \mathrm{taken}=2.5 \mathrm{hr} \end{gathered}$$

Hence, the time taken by Sajal to ride 75 km is 2.5 hr.

(ii) Given speed = 30 km/hr , time = $3\frac{1}{2}$ hr
using formula we have,

$$\begin{gathered} 30=\frac{\mathrm{distance}}{7/2} \\ \mathrm{distance}= 105 \mathrm{km} \end{gathered}$$

Hence, the distance covered by Sajal in $3\frac{1}{2}$ hours is 105 km.

Q24 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 24:

Explain the situations represented by the following distance-time graphs:

Answer 24:

 (a) Graph shows the uniform speed.
(b) Moves with uniform speed and then comes to rest.
(c) Moves with non uniform speed and then slowly comes to rest.

Q25 | Ex-23 | Class 8 | RS AGGARWAL | chapter 23 | Line Graphs and Linear Graphs

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Question 25:

Can there be a temperature-time graph as follows? Justify your answer.

Answer 25:

(i) Yes, temperature is directly proportional to time.
(ii) Yes, temperature decreases with time.
(iii) No, temperature can not change for a particular time.
(iv) Yes, temperature is constant.