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Example 14: Are 24, 28, 36, 48 in proportion?

Solution: We have, a, b, c and d are in proportion, if

product of extremes = product of means

That is, a × d = b × c Alternative Method: 24 6
Here, product of extremes = 24 × 48 = 1152 Ratio of 24 and 28 = 28 = 7 = 6 : 7

Product of means = 28 × 36 = 1008 Ratio of 36 and 48 = 36 = 3 = 3 : 4
48 4
So, product of extremes ≠ product of means Here, 6 : 7 ≠ 3 : 4

Hence, 24, 28, 36, 48 are not in proportion. Hence, 24, 28, 36, 48 are not in
proportion.
Example 15: If x : 21 : : 44 : 33, find the value of x.
Solution: In a proportion, we have

Product of extremes = product of means

x × 33 = 21 × 44
33 x = 21 × 44

21 44
×
x = = 28
33
Hence, x = 28

Example 16: The ratio of the girls to that of the boys in a school is 6:7. If the number of girls in
the school is 1260, find:
( a) The number of boys in the school.

( b) The total number of students in the school.

Solution: The ratio of girls to boys is 6 : 7

( a) Let the number of boys in the school be x. Therefore, 6 : 7 : : 1260 : x
6x = 7 × 1260 (Product of extremes = Product of means)

7 1260
×
x = = 1470
6
Thus, the number of boys in the school = 1470
( b) Total number of students = 1260 + 1470 = 2730

Quick Check

Shreya’s height is 144 cm while Rohan’s height is 128 cm and their weights are 45 kg and 36 kg respectively.
Are their heights and weights in proportion?

Example 17: Height of tower A is 1480 cm, while height of another tower B is 1560 cm. Their weights
are proportional to their heights. If tower A’s weight is 480 kg, then find the weight of tower B.

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