The Wonderful World of Science – Numerical Problems with Stepwise Solutions
CBSE Class 6 Science — Chapter 1: Numerical Problems with Stepwise Solutions
Content Bank — Important Symbols & Simple Formulas
- Length (l) — measured in metre (m) or centimetre (cm).
- Mass (m) — measured in kilogram (kg) or gram (g). (1 kg = 1000 g)
- Time (t) — measured in second (s), minute (min). (1 min = 60 s)
- Average rate =
change / time(e.g., growth rate = height change ÷ time). - Percentage (%) =
(part / whole) × 100. - Density idea (conceptual) — more mass in same space feels heavier; no complex formula needed for Class 6.
- Use
<sup>and<sub>for powers and chemical notation — e.g., H2O for water.
Ravi measures a plant and finds it is 45 cm tall. Express this height in metres.
- 1 metre (m) = 100 centimetre (cm).
- Height = 45 cm = 45 ÷ 100 m = 0.45 m.
A sample of soil weighs 250 g. Express this mass in kilograms (kg).
- 1 kg = 1000 g.
- Mass = 250 g = 250 ÷ 1000 kg = 0.25 kg.
An observation was taken at 2:15 pm and repeated after 90 minutes. What is the new time?
- 90 minutes = 1 hour 30 minutes.
- 2:15 pm + 1 hour 30 minutes = 3:45 pm.
- Answer: 3:45 pm.
A seedling was 4 cm tall on Monday and 9 cm tall on Saturday (5 days later). Calculate the average growth per day.
- Change in height = 9 cm − 4 cm = 5 cm.
- Time = 5 days.
- Average growth per day = 5 cm ÷ 5 days = 1 cm/day.
In a class activity, 18 out of 24 students observed that sugar dissolves faster in hot water. What percentage observed this?
- Percentage = (part / whole) × 100 = (18 / 24) × 100.
- (18 ÷ 24) = 0.75 → 0.75 × 100 = 75%.
In an experiment, sugar dissolves in hot water in 30 seconds and in cold water in 90 seconds. How many times faster is dissolving in hot water compared to cold?
- Rate ∝ 1 / time (faster when time is less).
- Speed ratio = 90 s ÷ 30 s = 3. So sugar dissolves 3 times faster in hot water.
Three students measured a table length as 120 cm, 118 cm and 122 cm. Find the average (mean) length.
- Sum = 120 + 118 + 122 = 360 cm.
- Average = 360 ÷ 3 = 120 cm.
If 4 plants need 8 litres of water per week, how much water do 10 plants need per week (same conditions)?
- Water per plant = 8 L ÷ 4 = 2 L per plant per week.
- For 10 plants = 10 × 2 L = 20 L per week.
One beaker contains 0.75 L of solution and another contains 750 mL. Are these volumes equal?
- 1 L = 1000 mL → 0.75 L = 0.75 × 1000 mL = 750 mL.
- Yes — both are 750 mL, so they are equal.
A sample had 50 seeds; 40 germinated. What percent germinated and what percent did not?
- Germinated percent = (40 / 50) × 100 = 80%.
- Did not germinate = 100% − 80% = 20%.
An observation started at 09:20 and ended at 11:05. How long did the activity run?
- From 09:20 to 11:05 = 1 hour 45 minutes.
- Convert to minutes if needed: 1 h 45 min = 60 + 45 = 105 minutes.
In a tray of 30 objects, 12 are smooth and 18 are rough. What is the ratio of smooth to rough?
- Ratio smooth : rough = 12 : 18. Simplify dividing by 6 → 2 : 3.
- Answer: 2 : 3.
Three trials of an experiment took 45 s, 50 s and 40 s. What is the average trial time?
- Sum = 45 + 50 + 40 = 135 s.
- Average = 135 ÷ 3 = 45 s.
If 5 students observe 3 insects each, how many insects were observed in total? If class has 30 students and each observes same number, total insects?
- First total = 5 × 3 = 15 insects.
- If each of 30 students observes 3 insects → 30 × 3 = 90 insects.
A student records an event lasting 2 minutes 20 seconds. Express this duration in seconds.
- 2 minutes = 2 × 60 s = 120 s. Add 20 s → 120 + 20 = 140 s.
An experiment uses 50 mL of solution for one setup. How much solution is needed for 6 setups?
- For 6 setups: 50 mL × 6 = 300 mL.
A plant's height increased from 10 cm to 12 cm in one week. What is the percentage increase?
- Increase = 12 − 10 = 2 cm.
- Percentage increase = (2 / 10) × 100 = 20%.
- Answer: 20%.
Convert 7.3 cm into millimetres (mm). (1 cm = 10 mm)
- 7.3 cm = 7.3 × 10 mm = 73 mm.
A student estimates there are about 475 grains of sugar in a jar. Round this estimate to the nearest hundred.
- Nearest hundred: 475 → 500 (because tens digit 7 ≥ 5).
- Answer: 500.
Water is H2O. If 3 water molecules are written, show correct notation and count of hydrogen and oxygen atoms.
- 3 molecules of H2O: write as 3 × H2O (or H2O × 3).
- Each molecule has 2 hydrogen (H) and 1 oxygen (O).
- Total hydrogen atoms = 3 × 2 = 6 H atoms; oxygen atoms = 3 × 1 = 3 O atoms.