Direct and Inverse Proportions, Ex- 12C

Question

7. A photograph of a bacteria enlarged 50000 times attains a length of 5 cm. The actual length of bacteria is
(a) 1000 cm
(b) 10^-3 cm
(c) 10^-4 cm
(d) 10^-2 cm

10. A car takes 2 hours to reach a destination by travelling at 60 km/hr. How long will it take while travelling at 80 km/hr?
(a) 1 hr 30 min
(b) 1 hr 40 min
(c) 2 hrs 40 min
(d) none of these

Can anyone please tell me the answers of question no. 7 and 10?

Answer 1

7. 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 20,000	5 ?

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

10. Consider the speed to be x and the time taken to be y.

If the speed increases, the time required to reach will decrease. Hence, they are in inverse proportion.

Two numbers x and y are said to be in inverse proportion when an increase in one quantity decreases the other quantity and vice versa.

xy = k or x = (1/y) k

where k is a constant.

Hence, x₁y₁ = x₂y₂

60 × 2 = 80 × y₂

y₂ = (60 × 2)/80

y₂ = 3/2

y₂ = 1.5 hours

Thus, 1.5 hours are required to reach the destination if the speed is increased to 80 km/hour.