The ratio of two numbers a and b is the fraction , usually expressed in reduced form. An alternative form involves a colon. The colon form is most frequently used when comparing three or more numbers to each other.

If ratio of salary of A:B is 2:3, then in terms of value we can write.

               A = 2x rs

               B = 3x rs

THIRD PROPORTIONAL

If  a : b = c : d, then c is called the third proportion to a and b.

Example: If 2, 5, x, 30 are in proportion, find the third proportional “x”.

Sol: Here x is third proportional. According to the concept 2/5 = x/30 → x = 12

FOURTH PROPORTIONAL

If a : b = c : d, then d is called the fourth proportional to a, b, c.

Example: Find the fourth proportional of the numbers 12, 48, 16.

Sol: Let fourth proportional is x.

Now as per the concept above the product of extremes should be equal to the product of the means → 12/48 = 16/x → x = 64.

Find the compound ratio of 3 : 5, 7 : 12 and 10 : 13.

a) 9 : 25                        b) 9 : 26                        c) 7 : 26                        d) 7 : 25

Solution:

Compound ratio means product of given ratios.

Required compound ratio = (3 / 5) × (7 / 12) × (10 / 13) = 7 / 26          Þ        7 : 26.

Answer: c

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