A photograph of a bacteria is enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
Solution:
Let the enlargement factor of the bacteria be x and the enlarged length of the bacteria be y.
| Number of times enlarged | Enlarged Length |
| 50,000 | 5 |
| 20,000 | ? |
The number of times the bacteria enlarges is directly proportional to the length attained.
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
x₂ / y₂ = x₁ / y₁
y₂ = (20000 × 5) / 50000
y₂ = 2
Thus, the enlarged length will be 2 cm.
Now, to calculate the actual length we know that the enlargement factor will be 1. Let the actual length be l
Using x₁ / y₁ = x₂ / y₂
50000 / 5 = 1 / l
l = 5 / 50000
l = 10-4
Thus, the actual length of the bacteria is 0.0001 cm.
☛ Check: NCERT Solutions for Class 8 Maths Chapter 13
Video Solution:
A photograph of a bacteria is enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
NCERT Solutions Class 8 Maths Chapter 13 Exercise 13.1 Question 5
Summary:
A photograph of a bacteria is enlarged 50,000 times attains a length of 5 cm as shown in the diagram. The actual length of the bacteria is 0.0001 cm. If the photograph is enlarged 20,000 times only, its enlarged length will be 2 cm.
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