untitled

25

2

21 16

or,

b b

or, 5 b 50
?b 10
Putting b 10 in equation (iii), we get, a 35
? The present age of father is 35 years, and that of son is 10 years.

Example 3. If a:b b:c, prove that.
2 2

(^222)
b c
a b
b c
a b




̧^
¹
·
̈
©
§
Solution : Given that, a:b b:c
?b^2 ac
Now,
2
(^22)
( )
( )
b c
a b
b c
a b


̧^
¹
·
̈
©
§


c
a
ca b c
aa b c
ac bc c
a ab ac
b bc c
a ab b
 
 
 
 
 
 
( 2 )
( 2 )
2
2
2
2
2
2
2 2
2 2
and
2
2
2 2
2 2
ac c
a ac
b c
a b




c
a
ca c
aa c


( )
( )
2 2
(^222)
b c
a b
b c
a b




̧^
¹
·
̈
©
? §
Example 4. If
d
c
b
a
, show that.
2 2
2 2
ac bd
ac bd
a b
a b




Solution : Let, k;
d
c
b
a
?a^ bkandc^ dk
Now,
1
1
( 1 )
( 1 )
( )
( )
2
2
2 2
2 2
2 2
2 2
2 2
2 2








k
k
b k
b k
bk b
bk b
a b
a b
and
1
1
( 1 )
( 1 )
2
2
2
2




˜ 
˜ 


k
k
bdk
bdk
bk dk bd
bk dk bd
ac bd
ac bd
.
ac bd
ac bd
a b
a b




?
2 2
2 2