7 th maths 1.5

7th Standard Mathematics — Chapter 1

Exercise 1.5 Solutions

1. Temperature Change Problem

One night in Kashmir, the temperature is -5°C. Next day the temperature is 9°C. What is the increase in temperature?

Solution:

• Night temperature = -5°C
• Next day temperature = 9°C
• Increase in temperature = 9°C - (-5°C) = 9 + 5 = 14°C

Answer: The increase in temperature is 14°C.

2. Net Charge Determination

An atom can contain protons (+ charge) and electrons (- charge). Determine the net charge:

1. 5 electrons and 3 protons → -5 + 3 = -2 (2 electrons)
2. 6 Protons and 6 electrons → +6 + (-6) = 0 (Neutral)
3. 9 protons and 12 electrons → +9 + (-12) = -3 (3 electrons)
4. 4 protons and 8 electrons → +4 + (-8) = -4 (4 electrons)
5. 7 protons and 6 electrons → +7 + (-6) = +1 (1 proton)

3. Celsius to Kelvin Conversion

Convert the following to Kelvin using the relation: K = T + 273

1. -275°C: K = -275 + 273 = -2 K
2. 45°C: K = 45 + 273 = 318 K
3. -400°C: K = -400 + 273 = -127 K
4. -273°C: K = -273 + 273 = 0 K

4. Bank Balance Problem

Find the amount left in the student's bank account (Initial balance = ₹ 690):

Transactions:

• Initial balance = ₹ 690
• (i) Deposit (+) = + ₹ 485 → Balance = 690 + 485 = ₹ 1175
• (ii) Withdrawal (-) = - ₹ 500 → Balance = 1175 - 500 = ₹ 675
• (iii) Withdrawal (-) = - ₹ 350 → Balance = 675 - 350 = ₹ 325
• (iv) Deposit (+) = + ₹ 89 → Balance = 325 + 89 = ₹ 414

Answer (iv): Balance after transactions = ₹ 414

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(v) If another ₹ 300 was withdrawn, what would the balance be?

New Balance = 414 - 300 = ₹ 114

Answer (v): The final balance would be ₹ 114.

5. Poet Tamizh Nambi's Pages Problem

A poet Tamizh Nambi lost 35 pages of his 'lyrics' when his file got wet in the rain.

1. If Tamizh Nambi wrote 5 pages per day, how many days' work did he lose?
   Total pages lost = 35
   Days lost = 35 ÷ 5 = 7 days
2. If 4 pages contained 1800 characters, how many characters were lost?
   Characters in 1 page = 1800 ÷ 4 = 450 characters
   Total characters lost = 35 × 450 = 15,750 characters
3. If Tamizh Nambi is paid ₹250 for each page produced, how much money did he lose?
   Money lost = 35 × ₹250 = ₹ 8,750
4. 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?
   Days required = 35 ÷ 7 = 5 days
5. Tamizh Nambi pays Kavimaan ₹ 100 per page for his help. How much money does Kavimaan receive?
   Money received by Kavimaan = 35 × ₹100 = ₹ 3,500

6. Riddle / Number Puzzle

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?

Solution:

Let the number be x.

Step-by-step equation:

[ (x + 2) × 5 - 10 ] ÷ 4 = 15

(x + 2) × 5 - 10 = 15 × 4

(x + 2) × 5 - 10 = 60

(x + 2) × 5 = 70

x + 2 = 70 ÷ 5

x + 2 = 14

x = 14 - 2 = 12

Answer: The number is 12.

7. Profit and Loss Problem

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?

Solution:

• Profit from 30 apples = 30 × ₹ 8 = + ₹ 240
• Loss from 50 pomegranates = 50 × ₹ 5 = - ₹ 250
• Net Amount = +240 - 250 = - ₹ 10

Answer: She incurs an overall loss of ₹ 10.

8. Water Level Change Problem

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 at the end of this period?

Solution:

• Water level change per week = -3 inches
• Total weeks = 6
• Total change = 6 × (-3) = -18 inches

Answer: The water level decreased by 18 inches (change of -18 inches).

9. Timeline / Historical Problem

Buddha was born in 563 BC(BCE) and died in 483 BC(BCE). Was he alive in 500 BC(BCE)? Find his lifetime.

Solution:

• Birth Year = -563
• Death Year = -483

1. Was he alive in 500 BC?

Since 500 BC (-500) falls between 563 BC (-563) and 483 BC (-483), Yes, he was alive in 500 BC.

2. Lifetime calculation:

Lifetime = Death Year - Birth Year = -483 - (-563) = -483 + 563 = 80 years.

Answer: Yes, he was alive in 500 BC. His total lifetime was 80 years.