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earning : Sami’s earning = 1500 : 2500 = 3 : 5. Hence, Roni’s : Soni’s : Sami’s

earning = 2 : 3 : 5.

If two ratios are of the form a : b and b : c, they can be put in the form a : b : c. This

is called successive ratio. Any two or more than two ratios can be put in this form. It

is to be noted that if two ratios are to be put in the form a : b c, antecedent of the first

ratio and subsequent of the second ratio are to be equal. Such as, if two ratios 2 : 3

and 4 : 3 are to be put in the form a : b : c the subsequent quantity of first ratio is to

be made equal to antecedent quantity of the second ratio. That is those quantities are

to be made equal to their L.C.M.

Here, 8 : 12

12

8

3 4

2 4

3

2

2 : 3

u

u

Again, 12 : 9

9

12

3 3

4 3

3

4

4 : 3

u

u

Therefore, if the ratios 2 : 3 and 4 : 3 are put in the form, a : b : c will be 8 : 12 : 9.

It is to be noted that if the earning of Sami in the above example is 1125, the ratio of

their earnings will be 8 : 12 : 9.

Example 12. If a, b, c are quantities of same kind and a : b = 3 : 4, b : c = 6 : 7, what

will be a : b : c?

Solution :

12

9

4 3

3 3

4

3

b

a

u

u

and

14

12

7 2

6 2

7

6

c

b

u

u

[ L.C.M. of 4 and 6 is 12]

?a : b : c = 7 : 12 : 14.

Example 13. The ratio of angles of a triangle is 3 : 4 : 5. Express the angles i n

degree.

Solution : Sum of three angles = 180 º

et the angles, according to given ratio, be 3L x, 4 xand 5x.

According to the problem, 3 x + 4x + 5x = 180 º or, 12x = 180 º or, x = 15º

Therefore, the angles are 3x = 3 × 15 º = 45º

4 x = 4 × 15 º = 60º

and 5x = 5 × 15 º = 75º

Example 14. If the sides of a square increase by 10%, how much will the area be

increased in percentage ?