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Solution: Given that, height of tower A = 1480 cm, height of tower B = 1560 cm, and weight of
tower A = 48 kg.

Let the weight of tower B be x kg.
Since their weights are proportional to their heights.

Therefore, 1480 cm : 1560 cm : : 480 kg : x kg
1480 : 1560 : : 480 : x

Therefore, 1480 × x = 1560 × 480 (Product of extremes = Product of means)
1560 480
×
x = = 505.945 ≈ 506
1480
Thus, the weight of tower B is 506 kg approx.

Example 18: Arun made a model of the building in which he lives of height 105 cm and a model
of his mother of height 35 cm. The actual heights of the building and his mother are proportional
to their model’s heights. If the height of his mother is 150 cm then, find the actual height of the
building.
Solution: Height of building’s model = 105 cm
Height of mother’s model = 35 cm

Actual height of the mother = 150 cm
Let the actual height of the building be x cm
Since, the heights are proportional.

Therefore, 105 cm : 35 cm : : x cm : 150 cm
105 : 35 : : x : 150
Therefore, 35 × x = 105 × 150 (Product of extremes = Product of means)

105 150
×
x = = 450 cm = 4.5 m
35
Thus, the actual height of the building is 4.5 m.
Example 19: A map is given with a scale of 1 cm = 500 km. What is the actual distance between
the two places in km, if the distance in the map is 2.5 cm?

Solution: Let the actual distance between two places = x km
Therefore,
1 cm : 2.5 cm = 500 km : x km
1: 2.5 = 500 : x

1 × x = 2.5 × 500 (Product of extremes = Product of means)
⇒ x = 1250
Thus, the actual distance between two places is 1250 km if the distance in the map is 2.5 cm.

Continued Proportion

Three numbers are said to be in continued proportion if the ratio of the first and the second
number is equal to the ratio of the second and the third number.

209 Ratio and Proportion