Real numbers in daily life: temperature, profit and loss

Numbers you use every day

Your book lists where real numbers work: science and engineering, medicine, environmental science, computing, navigation, surveying and statistics. This section takes two everyday cases: temperature and money.

Three scales measure temperature. Water freezes at 0 °C, 32 °F, 273 K and boils at 100 °C, 212 °F. Convert with K = °C + 273 and °C = 5/9 (°F − 32).

In trade, profit = selling price − cost price and loss = cost price − selling price. Both percentages are taken on the cost price: profit/CP × 100.

Partners share profit in the ratio of their investments. Simple profit gives rate = profit × 100 / (time × principal).

Percentages of profit or loss are always out of the cost price, never the selling price.

Key terms

Kelvin

The scientific temperature scale.

Cost price (CP)

The base for profit and loss percentages.

Profit %

Profit as a share of cost.

Ratio share

Splitting a profit between partners.

Short questions with model answers

1. Q1. Example 10: convert 98.6 °F to Celsius and Kelvin.

   • °C = 5/9 (98.6 − 32) = 5/9 × 66.6 = 37
   • K = 37 + 273 = 310

   37 °C and 310 K.

2. Q2. Example 13: Rs. 4,50,000 profit shared in the ratio 4 : 7 : 14. Find each share.

   • 4 + 7 + 14 = 25
   • 4/25 × 450000 = 72000; 7/25 × 450000 = 126000; 14/25 × 450000 = 252000

   Saleem Rs. 72,000; Nadeem Rs. 126,000; Tanveer Rs. 252,000.

Common mistakes

• ✗ Profit % = 260/6850 × 100.

  ✓ Divide by the cost price: 260/6590 × 100 = 3.94%.

• ✗ °C = 5/9 × 98.6.

  ✓ Subtract 32 first: 5/9 × (98.6 − 32) = 37.

• ✗ Dividing 4,50,000 by 3 because there are three partners.

  ✓ Shares follow the ratio: divide by 4 + 7 + 14 = 25 parts.

MCQs

1. 1. The sum of two numbers is 8 and their difference is 2. The numbers are:

   1. (a) 6 and 2
   2. (b) 5 and 3
   3. (c) 4 and 4
   4. (d) 7 and 1
   Show answer

   (b) 2a = 10 → a = 5, b = 3 (Example 9).

2. 2. 37 °C in kelvin is:

   1. (a) 236 K
   2. (b) 98.6 K
   3. (c) 310 K
   4. (d) 273 K
   Show answer

   (c) K = 37 + 273 = 310 (Example 10).

3. 3. Umair bought a book for Rs. 850 and sold it for Rs. 720. His loss % is:

   1. (a) 18.06%
   2. (b) 13%
   3. (c) 130%
   4. (d) 15.29%
   Show answer

   (d) 130/850 × 100 = 15.29% (Example 12).

4. 4. Simple profit Rs. 3840 on Rs. 6400 for 12 years. The rate is:

   1. (a) 5%
   2. (b) 6%
   3. (c) 4%
   4. (d) 60%
   Show answer

   (a) 3840 × 100 / (12 × 6400) = 5% (Example 14).

5. 5. Water boils at:

   1. (a) 100 °F
   2. (b) 212 °F
   3. (c) 273 °C
   4. (d) 32 °C
   Show answer

   (b) 100 °C = 212 °F (figure, p. 15).

Quick revision

• K = °C + 273 and °C = 5/9 (°F − 32); 98.6 °F = 37 °C = 310 K.
• Profit % and loss % are both taken on the cost price.
• A ratio share is part/sum of parts × total.