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

**Ex 15.1 Class 8 Maths 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 pm?**

**(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 the two times?**

**(d) What was the temperature at 1:30 pm? How did you arrive at your answer?**

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

**Solution:**

(a) The patient’s temperature at 1 pm was 36.5°C

(b) The patient’s temperature was 38.5°C at 12:00 noon.

(c) The patients temperature was 36.5°C at 1 pm and 2 pm.

(d) The temperature at 1:30 pm was 36.5°C. We have taken the mid value of 1 pm. and 2 pm, i.e., 1:30 p.m and proceed perpendicularly upwards to meet the horizontal line showing 36.5°C.

(e) During 9 am to 10 am and 10 am to 11 am, the temperature showed upwards trend.

**Ex 15.1 Class 8 Maths 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 the sales in 2002 and 2006.**

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

**Solution:**

(a) The sales in the year 2002 was ₹ 4 crore and in the year 2006 was ₹ 8 crore.

(b) The sales in the year 2003 was ₹ 7 crore and in 2005 was ₹ 10 crore.

(c) Sales in 2002 = ₹ 4 crore

Sales in 2006 = ₹ 8 crores

Difference = ₹ (8 – 4) crore = ₹ 4 crore.

(d) The greatest difference between the sales was in the year 2005, as compared to previous year.

**Ex 15.1 Class 8 Maths 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 the 3rd week?**

**(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:**

(a) The height of plant A (i) after 2 weeks was 7 cm (ii) after 3 weeks was 9 cm.

(b) The height of plant B (i) after 2 weeks was 7 cm (ii) after 3 weeks was 10 cm.

(c) Plant A grew 7 cm to 9 cm i.e, 2 cm.

(d) Plant B grew 7 cm to 10 cm i.e., 3 cm.

(e) Plant A grew most in a 2nd week i.e., 5 cm.

(f) Plant B grew the least in a first week i.e., 1 cm.

(g) Yes, the two plants grew the same height at the end of 2nd week i.e., 7 cm.

**Ex 15.1 Class 8 Maths 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) On Tuesday, Friday and Sunday, the forecast temperature was the same as the actual temperature i.e., 20°C, 15°C and 35°C respectively.

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

(c) The minimum actual temperature during the week was 17.5°C

(d) On Thursday, the actual temperature differed the most from the forecast temperature

i.e., 22.5°C – 15°C = 7.5°C.

**Ex 15.1 Class 8 Maths Question 5.**

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

**(a) The number of days a hillside city recovered show in different years.**

Year | 2003 | 2004 | 2005 | 2006 |

Days | 8 | 10 | 5 | 12 |

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

Year | 2003 | 2004 | 2005 | 2006 | 2007 |

Number of men | 12 | 12.5 | 13 | 13.2 | 13.5 |

Number of women | 11.3 | 11.9 | 13 | 13.6 | 12.8 |

**Solution:**

**Ex 15.1 Class 8 Maths Question 6.**

**A courier-person cycle from a town to a neighbouring suburban area to deliver a parcel to the 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 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) Scale taken on time-axis i.e., the x-axis is 4 units = 1 hour

(b) Total time taken by the person for the total journey is 3 hours 30 minutes.

(c) The place of the merchant is at a distant of 22 km from the town.

(d) Yes, this is indicated by the horizontal part of the graph clearly the person stopped from 10 am to 10:30 am.

(e) He rode fastest between 8 am and 9 am.

**Ex 15.1 Class 8 Maths Question 7.**

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

**Solution:**

(i) It represents a time-temperature graph where temperature increases as the time increase.

(ii) It shows a time-temperature graph where temperature decreases as the time increases.

(iii) It does not represent a time-temperature graph. Here the temperature is increasing at the constant time which is not possible.

(iv) It represents a time-temperature graph where the temperature remains constant when the time is increasing.