Page 183 - Maths Class 06

In a statement of proportion, the first and fourth terms are known as extreme terms. The second and third
terms are known as middle terms.
In general, a : b :: c : d

Means
Extremes

In proportion, the product of extremes = product of means, i e. . ad = bc.
EXAMPLE 1. Are the ratios 20 mL : 30 mL and 40 litre : 50 litre in proportion?
SOLUTION : 20 mL : 30 mL = 2 : 3

And 40 litre : 50 litre = 4 : 5
As, 2 : 3 ¹ 4 : 5

So, 20 : 30 ¹ 40 : 50.
Therefore, the ratios 20 mL : 30 mL and 40 litre : 50 litre are not in proportion.
EX AM PLE 2. Find x, if x, 5, 30, 25 are in pro por tion.

SOLUTION : Since x, 5, 30, 25 are in pro por tion.
5 15´
\ x × 25 = 5 × 15 or x = or x = 3.
25
Hence, the value of x is 3.

EX AM PLE 3. Find a if the quan ti ties 4, 5, 16, a are in pro por tion.
SOLUTION : Given the num bers are in pro por tion.

\ 4 : 5 :: 16 : a
4 × a = 5 × 16 [ Q Product of extremes = Product of means]
5 16´
or a =
4

or a = 20
Hence, the value of a is 20.

Continued Proportion
Three numbers a b c, , are said to be in continued proportion if a b b, , and c are in proportion.
a b
2
i e. ., = Þ b = ac
b c
If a b c, , are in continued proportion then b is known as the mean proportion of a and c and c is known as
the third proportion.

EX AM PLE 4. Determine if the fol low ing are in pro por tion:
(a) 3, 12, 5, 20 (b) 10, 20, 30, 40
SOLUTION : (a) 3, 12, 5, 20
3 5
Ratio of 3 to 12 = = 1 : 4 Ratio of 5 to 20 = = 1 : 4
12 20

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