# Class 8 NCERT Solutions – Chapter 15 Introduction to Graphs – Exercise 15.1

**Question 1: The following graph shows the temperature of a patient in a hospital, recorded every hour.**

**(i) What was the patientâ€™s temperature at 1 p.m.?**

**Solution:**

The patient’s temperature at 1 p.m. was 36.5

^{o}C.

**(ii) When was the patientâ€™s temperature 38.5Â° C?**

**Solution:**

The patient’s temperature was 38.5

^{o}C at 12 noon.

**(iii) The patientâ€™s temperature was the same two times during the period given. What were these two times?**

**Solution:**

Patient’s temperature at 2 p.m. was the same as the patient’s temperature at 1 p.m. (36.5

^{o}C).

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

**Solution:**

Patient’s temperature was 36.5

^{o}C at 1:30 p.m.

The line in between 1 p.m. and 2 p.m. represents 1:30 p.m. And the line in between 36^{o}C and 37^{o}C

represents 36.5^{o}C. Therefore the temperature at 1:30 p.m. was 36.5^{o}C.

**(v) During which periods did the patientsâ€™ temperature showed an upward trend?**

**Solution:**

Patient’s temperature showed an upward trend between 9 a.m. and 11 a.m. and also the patient’s

temperature showed an upward trend between 2 p.m. and 3 p.m. for the second time.

**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?**

**Solution:**

(i) Sales in 2002 was 4 crore rupees.

(ii) Sales in 2006 was 8 crore rupees.

**(b) What were the sales in (i) 2003 (ii) 2005?**

**Solution:**

(i) sales in 2003 were 7 crore rupees.

(ii) sales in 2005 were 10 crore rupees.

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

**Solution:**

The difference between the sales in 2002 and 2006 is 4 crore rupees.

Explanation:Sales in 2002 was 4 crore rupees Sales in 2006 were 8 crore rupees difference between 8 crore and 4 crore rupees is 4 crore rupees therefore, the difference between the sales in 2002 and 2006 is 4 crore rupees.

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

**Solution:**

In 2005 there was the greatest difference between the sales as compared to its previous year (2004).

**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 **in** the following graph.**

**(a) How high was Plant A after (i) 2 weeks (ii) 3 weeks?**

**Solution:**

(i) Plant A was 7 cm’s high after 2 weeks.

(ii) Plant A was 9 cm’s high after 3 weeks.

**(b) How high was Plant B after (i) 2 weeks (ii) 3 weeks?**

**Solution:**

(i) Plant B was 7 cm’s high after 2 weeks.

(ii) Plant B was 10 cm’s high after 3 weeks.

**(c) How much did Plant A grow during the 3rd week?**

**Solution:**

Plant A’s height after 2 weeks was 7 cm’s and

Plant A’s height after 3 weeks was 9 cm’s

therefore, Plant A grew 2 cm’s in the 3rd week (which is 9 cm’s – 7 cm’s).

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

**Solution:**

Plant B’s height after 2 weeks was 7 cm’s and

Plant B’s height after 3 weeks was 10 cm’s

therefore, Plant B grew 3 cm’s from the end of the 2nd week to the end of the 3rd week (which is 10 cm’s – 7 cm’s).

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

**Solution:**

2nd week.

Explanation:Plant A grew 2 cm’s in 1st week, 5 cm’s in 2nd week, 2 cm’s in 3rd week. Therefore, Plant A grew most in 2nd week.

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

**Solution:**

1st week.

Explanation:Plant B grew 1 cm in 1st week, 6 cm’s in 2nd week, 3 cm’s in 3rd week. Therefore, Plant B grew Least in 1st week.

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

**Solution:**

Yes, after 2 weeks both the plants are at the same height (which is 7 cm).

**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?**

**Solution:**

On Tuesday, Friday, Sunday forecast temperature was the same as the actual temperature.

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

**Solution:**

35

^{o}C was the maximum forecast temperature during the week.

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

**Solution:**

15

^{o}C was the minimum actual temperature during the week.

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

**Solution:**

On Thursday, the difference between actual temperature and forecast temperature is 15

^{o}C and it is

the maximum among all the days.

**Question 5: Use the tables below to draw linear graphs.**

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

Year |
2003 |
2004 |
2005 |
2006 |
---|---|---|---|---|

Days |
8 |
10 |
5 |
12 |

**Solution:**

**(b) Population (in thousands) of men and women in a village in 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:**

**Question 6: A 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?**

**Solution:**

4 Units = 1 hour

Therefore, 1 Unit = 1/4 hour

1 Unit = 15 mins.

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

**Solution:**

The person traveled from 8:00 a.m. to 11:30 a.m.

Therefore, the person took 3 hours and 30 mins to travel.

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

**Solution:**

The distance between the place of a merchant from the town is 22 km.

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

**Solution:**

Yes, the person stopped on his way.

In between 10:00 a.m. and 10:30 a.m., his distance from the town remained the same.

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

**Solution:**

In between 8:00 a.m. and 9:00 a.m. (he traveled 10 km during this period and it is the maximum).

**Question 7: Can there be a time-temperature graph as follows? Justify your answer.**

**(i)**

**Solution:**

Yes, this graph shows the raise in temperature with respect to time.

**(ii)**

**Solution:**

Yes, this graph shows the decrease in temperature with respect to time.

**(iii)**

**Solution:**

No, Temperature cannot have different values at a given time.

**(iv)**

**Solution:**

Yes, this graph says the temperature is constant with respect to time.

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