NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 15 |

Chapter Name |
Introduction to Graphs |

Exercise |
Ex 15.1 |

Number of Questions Solved |
7 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1

**Question 1.**

The following graph shows the temperature of a patient in a hospital, recorded every hour.

**(a)** What was the patient’s temperature at 1 p.m.?

**(b)** When was the patient’s temperature 38.5°C?

**(c)** The patient’s temperature was the same two times during the period given. What were these two times?

**(d)** What was the temperature at 1.30 p.m.? How did you arrive at your answer?

**(e)** During which periods did the patient’s temperature showed an upward trend?

**Solution.**

**(а)** The patient’s temperature at 1 p.m. was 36.5°C.

**(b)** The patient’s temperature was 38.5°C at 10.50 a.m. and 12 noon.

**(c)** The two times when the patient’s temperature was the same were 1 p.m. and 2 p.m.

**(d)** The temperature at 1.30 p.m. was 36.5°C.

From the graph, we see that the temperature was constant from 1 p.m. to 2 p.m. Since 1.30 p.m. comes in between 1 p.m. and 2 p.m., therefore we arrived at our answer.

**(e)** The patient’s temperature showed an upward trend during the periods 9 a.m. to 10 a.m., 10 a.m. to 11 a.m. and 2 p.m. to 3 p.m.

**Question 2.**

The following line graph shows the yearly sales figures for a manufacturing company.

**(a)** What were the sales in

**(i)** 2002

**(ii)** 2006?

**(b)** What were the sales in

**(i)** 2003

**(ii)** 2005?

**(c)** Compute the difference between sales in 2002 and 2006.

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

**Solution.**

**(а)** The sales in

**(i)** 2002 were ₹ 4 crores and in

**(ii)** 2006 were ₹ 8 crores.

**(b)** The sales in

**(i)** 2003 were ₹ 7 crores and in

**(ii)** 2005 were ₹ 10 crores.

**(c)** The difference between the sales in 2002 and 2006

= ₹ 8 crores – ₹ 4 crores = ₹ 4 crores

**(d)** The difference between sales in 2002 and 2003

= ₹ 7 crores – ₹ 4 crores = ₹ 3 crores

The difference between sales in 2003 and 2004

= ₹ 7 crores – ₹ 6 crores = ₹ 1 crore

The difference between the sales in 2004 and 2005

= ₹ 10 crores – ₹ 6 crores = ₹ 4 crores

The difference between sales in 2005 and 2006

= ₹ 10 crores – ₹ 8 crores = ₹ 2 crores

Therefore, in year 2005 the difference between the sales as compared to its previous year was the greatest.

**Question 3.**

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 3 weeks. The results are shown by the following graph.

**(a)** How high was Plant A after

**(i)** 2 weeks

**(ii)** 3 weeks?

**(b)** How high was Plant B after

**(i)** 2 weeks

**(ii)** 3 weeks?

**(c)** How much did Plant A grow during

**(d)** How much did Plant B grow from the end of the 2nd week to the end of the 3rd week?

**(e)** During which week did Plant A grow most?

**(f)** During which week did Plant B grow least?

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

**Solution.**

**(а)** The Plant A

after** (i)** 2 weeks was 7 cm high and

after **(ii)** 3 weeks was 9 cm high.

**(b)** The Plant B

after** (i)** 2 weeks was 7 cm high and

after** (ii)** 3 weeks was 10 cm high.

**(c)** The Plant A grew 9 cm – 7 cm = 2 cm during the 3rd week.

**(d)** From the end of the 2nd week to the end of the 3rd week, Plant B grew

= 10 cm – 7 cm = 3 cm.

**(e)** The Plant A grew in 1st week

= 2 cm – 0 cm = 2 cm

The Plant A grew in 2nd week

= 7 cm – 2 cm = 5 cm

The Plant A grew in 3rd week

= 9 cm – 7 cm = 2 cm

Therefore, Plant A grew mostly in the second week.

**(f)** Plant B grew in 1st week

= 1 cm – 0 cm = 1 cm

Plant B grew in 2nd week

= 7 cm – 1 cm = 6 cm

Plant B grew in 3rd week

= 10 cm – 7 cm = 3 cm

Therefore, Plant B grew least in the first week.

**(g)** At the end of 2nd week, the two plants shown here were of the same height.

**Question 4.**

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

**(a)** On which days was the forecast temperature the same as the actual temperature?

**(b)** What was the maximum forecast temperature during the week?

**(c)** What was the minimum actual temperature during the week?

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

**Solution.**

**(a)** The forecast temperature was the same as the actual temperature on Tuesday, Friday and Sunday.

**(b)** The maximum forecast temperature during the week was 35°C.

**(c)** The minimum actual temperature during the week was 15°C.

**(d)**

Therefore, the actual temperature differed the most from the forecast temperature on Thursday.

**Question 5.**

**Use the tables below to draw linear graphs.**

**(a)** The number of days a hill side city received snow in different years.

**(b) **Population (in thousands) of men and women in a village in different years.

**Solution.**

**(a)**

**(b)**

**Question 6.**

Courier-person cycles from a town to a neighboring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.

**(a)** What is the scale taken for the time axis?

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

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

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

**(e)** During which period did he ride fastest?

**Solution.**

**(a)** The scale taken for the time axis is 4 units = 1 hour.

**(b)** The time taken by the person for the travel 8 a.m. to 11.30 a.m. = \(3\frac { 1 }{ 2 } \) hours.

**(c)** The place of the merchant from the town in 22 km.

**(d)** Yes. This is indicated by the hori¬zontal part of the graph (10 a.m. – 10.30 a.m.)

**(e)** He rides fastest between 8 a.m. and 9 a.m. (As line is more steep in this period).

**Question 7.**

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

**Solution.**

**(i)** Yes; it can be

It shows a time-temperature graph. It shows an increase in temperature with an increase in time.

**(ii)** Yes; it can be

It shows a time-temperature graph.

It shows a decrease in temperature with increase in time.

**(iii)** It cannot be a time-temperature graph because it shows infinitely many different temperatures at one particular time which is not possible.

**(iv)** Yes; it can be

It shows a time-temperature graph,

It shows a fixed temperature at different times.

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