(1) If
then bc = ad
This property is known as INVERTENDO.
(2) If
, then ad = bc

(3) If we add 1 to both sides of
then 
This property is known as COMPONENDO.
(4) If we subtract 1 from both sides of
then

(5) If result (3) is divided by the result (4), then

or 

This property is known as COMPONENDO & DIVIDENDO.
(6) If
, then each of these ratios equals
where l,m,n are real numbers.
Let 
Similarly c = dk and e = fk
(This method is called k-method. It will be freely used in this topic.)
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(i)
, (ii) 
1st method:
9x - 4x = 13y + 11y
5x = 24 y

(Componendo and Dividendo)
Again 


(ii) 
2nd Method:
from 1st method
and y = 5k
(i)




, (ii) 
3rd Method:
We can also solve the problem by substituting
and get the same result.
If a : b = c : d, then prove that 
Let 
or a = bk.
Similarly, c = dk
LHS
…(i)
RHS 

…(ii)
From (i) and (ii),
LHS = RHS Hence proved.![]()
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7 + x, 22 + x and 62 + x are in continued proportion.
(22 + x)2 = (7 + x) (62 + x)
484 + 44x + x2 = x2 + 69x + 434
44x - 69x = 434 - 484-25x = -50
x = 2
2 should be added.
If 
show that 
Let 
(equal ratios results)

…(i)
Similarly, we can obtain
…(ii)
From (i) and (ii), we get the required result

