Exercise 1.5

Exercise 1.5

1. One night in Kashmir, the temperature is −5º C. Next day the temperature is 9º C. What is the increase in temperature?

9°C – (–5°C) = 9°C + 5°C = 14°C

2. An atom can contain protons which have a positive charge ( +) and electrons which have a negative charge ( −) . When an electron and a proton pair up, they become neutral (0) and cancel the charge out. Now, Determine the net charge:

(i) 5 electrons and 3 protons → −5 + 3 = −2 that is 2 electrons 

(ii) 6 Protons and 6 electrons →  +6 – 6 = 0

(iii) 9 protons and 12 electrons → +9 –12 = –3 that is electrons 

(iv) 4 protons and 8 electrons → +4 – 8 = –1 that is electrons 

(v) 7 protons and 6 electrons → +7 – 6 = +1 that is proton (+)

3. Scientists use the Kelvin Scale (K) as an alternative temperature scale to degrees

Celsius (°C) by the relation T º C = ( T + 273) K.

Convert the following to kelvin:

(i) −275° C (ii) 45° C (iii) −400° C (iv) −273° C

(i) –275° C

(–275 + 273) K = –2° K

(ii) 45°C

(45 + 273) K = 318° K

(iii) –400° C

(–400 +273) K = 127° K

(iv) –273°C

(–273 + 273)K = 0° K

4. Find the amount that is left in the student’s bank account, if he has made the following transaction in a month. His initial balance is ₹ 690.

(i) Deposit ( +) of ₹ 485

(ii) Withdrawal ( −) of ₹ 500

(iii) Withdrawal ( −) of ₹ 350

(iv) Deposit ( +) of ₹ 89

(v) If another ₹ 300 was withdrawn, what would the balance be?

(i) Deposit (+) of ₹ 485 ?

₹ 690 + ₹ 485 = ₹ 1175

(ii) Withdrawal (–) of ₹ 500 ?

₹ 1175 – ₹ 500 = ₹ 675

(iii) Withdrawal (–) of ₹ 350

₹ 675 – ₹ 350 = ₹ 325 

(iv) Deposit of (+) ₹ 89

₹ 325 + ₹ 89 = ₹ 414

(v) If another ₹ 300 was withdrawn, what would the balance be?

₹ 414 – ₹ 300 = ₹ 114

The balance would be = ₹ 114

5. A poet Tamizh Nambi lost 35 pages of his ‘lyrics’ when his file had got wet in the rain. Use integers, to determine the following:

(i) If Tamizh Nambi wrote 5 page per day, how many day’s work did he lose?

35 ÷ 5 = 7 days

(ii) If four pages contained 1800 characters, (letters) how many characters were lost?

4 pages contained characters = 1800

∴ 35 pages contained characters = [ 1800 × 35 ] / 4 = 15750

15750 characters were lost

(iii) If Tamizh Nambi is paid ₹250 for each page produced, how much money did he lose?

Paid money for 1 page = ₹ 250

Paid money for 35 pages = ₹ 250 × 35 = ₹ 8750

 He lost = ₹ 8750

(iv) If Kavimaan helps Tamizh Nambi and they are able to produce 7 pages per day, how many days will it take to recreate the work lost?

Number of days it will take to recreate the work lost = 35 ÷ 7 = 5 days

(v) Tamizh Nambi pays kavimaan ₹ 100 per page for his help. How much money does kavimaan receive?

Kavimaan receives money = ₹ 35 × 100 = ₹ 3500

6. Add 2 to me. Then multiply by 5 and subtract 10 and divide now by 4 and I will give you 15! Who am I?

Add 2 to me, multiply by 5 and subtract 10 and divide by 4 = 15 

[ (x+2)5 – 10 ] / 4 = 15

5x + 10 – 10 = 60

 5x = 60

 x = 60 / 5 = 12

The number is 12.

7. Kamatchi, a fruit vendor sells 30 apples and 50 pomegranates. If she makes a profit of ₹ 8 per apple and loss ₹ 5 per pomegranate, what will be her overall profit(or)loss?

Number of apples = 30

Profit on apples = ₹ 30 × 8 = ₹240

Number of pomegranates = 50

Loss on pomegranates = ₹ 50 × 5 = ₹ 250

 Loss = 250

 Profit = ₹ 240

 Over all loss = ₹ 10

8. During a drought, the water level in a dam fell 3 inches per week for 6 consecutive weeks. What was the change in the water level in the dam at the end of this period?

Water level decrease per week = 3 inches

Water level decrease in 6 weeks = 3 × 6 = 18 inches

Water level decrease 18 inches in 6 weeks

9. Buddha was born in 563 BC(BCE) and died in 483 BC(BCE). Was he alive in 500 BC(BCE)? and find his life time. (Source: Compton’s Encylopedia)

Buddha was bom in 563 BC (BCE) died in 483 BC (BCE)

 500 BC (BCE) is in between 563 BC and 483 BC

∴ Yes. He alive in 500 BC (BCE)

Life: 80 year.

10. A young boy has got fever. The following chart shows how his temperature varies each day in a week. M→up 3° C, T→up 2° C, W→ Down 2° C, Th→ up 2° C, F→ Down 1° C, S→ up 2° C What was the average daily variation in his temperature?

(Average = Total change in temperature / Number of days)

Total change in temperature = +3 +2 –2 + 2 –1 + 2

                                            = 9 – 3 = 6

Number of days = 6

Average = Total change in temperature / Number of days

= 6 / 6 = 1

Average = 1

ANSWERS

Exercise 1.5

1. 14˚c

2. (i) −2 (ii) 0 (iii) −3 (iv) −4 (v) 1

3. (i) −2 k (ii) 318°k (iii) −127° k (iv) 0°k

4. (i) ₹1175 (ii) ₹675 (iii) ₹325 (iv) ₹414 (v) ₹114

5. (i) 7 days (ii) 15,750 characters (iii) ₹8750 (iv) 5 days (v) ₹3,500 6. 12 

7. Loss of ₹10

8. decrease of 18 inches

9. yes; 80 years