Suppose 2 kg of sugar contains 9 × 106 crystals
How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?
Solution:
Given that, 2 kg of sugar contains 9 × 106 crystals
(i) Let the amount of sugar be x and the number of crystals be y
| Amount of sugar | Number of crystals |
| 2 | 9 × 106 |
| 5 | ? |
More the amount of sugar more will be the number of crystals. Hence this is a direct proportion.
Two numbers x and y are said in direct proportion if, the relationship between two quantities is such that if we increase one, the other will also increase, and if we decrease one the other quantity will also decrease.
x/y = k, x = ky
where k is a constant.
Thus, x₁ / y₁ = x₂ / y₂
2 / (9 × 106) = 5 / y₂
2 × y₂ = 9 × 106 × 5
y₂ = (9 × 106 × 5) / 2
y₂ = 22.5 × 106
y₂ = 2.25 × 107
Hence there are 2.25 × 107 crystals.
(ii)
| Amount of sugar | Number of crystals |
| 2 | 9 × 106 |
| 1.2 | ? |
x₁/y₁ = x₂/y₂
2/(9 × 106) = 1.2/y₂
2 × y₂ = 9 × 106 × 1.2
y₂ = (9 × 106 × 1.2)/2
y₂ = 5.4 × 106
Hence there are 5.4 × 106 crystals.
☛ Check: NCERT Solutions for Class 8 Maths Chapter 13
Video Solution:
Suppose 2 kg of sugar contains 9 × 106 crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?
NCERT Solutions Class 8 Maths Chapter 13 Exercise 13.1 Question 7
Summary:
Suppose 2 kg of sugar contains 9 × 106 crystals. The number of sugar crystals that are there in (i) 5 kg of sugar is 2.25 × 107 (ii) 1.2 kg of sugar is 5.4 × 106
☛ Related Questions:
- Following are the car parking charges near a railway station up to: 4 hours ₹60 8 hours ₹100 12 hours ₹140 24 hours ₹180 Check if the parking charges are in direct proportion to the parking time.
- A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
- In question (2), above if 1 part of red pigment requires 75 ml of base, how much red pigment should we mix with 1800 ml of base?
- A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
visual curriculum