Question

If m : n = 3 : 4 and n : o = 8 : 9, then m : o is

Answer 1

Given :-

m : n = 3 : 4

n : o = 8 : 9

To find :-

m : o

Solution :-

Given that

m : n = 3 : 4

=> m / n = 3 / 4

=> m / n = (3/4)×(2/2)

=> m / n = (3×2)/(4×2)

=> m / n = 6 / 8

Therefore, m : n = 6 : 8

n : o = 8 : 9

m / o = ( m / n )× (n / o )

=> m / o = (6/8)×(8/9)

=> m / o = 6/9

=> m / o = 2/3

Therefore, m : o = 2 : 3

Alternative Method :-

Given that

m : n = 3 : 4

=> m / n = 3 / 4

=> m / n = (3/4)×(2/2)

=> m / n = (3×2)/(4×2)

=> m / n = 6 / 8

Therefore, m : n = 6 : 8

and

n : o = 8 : 9

Now,

m : n = 6 : 8

n : o = 8 : 9

______________

m : n : o = 6 : 8 : 9

______________

Therefore, m : o = 6 : 9

=> m / o = 6 / 9

=> m / o = 2 / 3

=> m : o = 2 : 3

Answer :-

m : o = 2 : 3

Used formulae:-

→ a : b can be written as a / b

Answer 2

Given,

m : n = 3 : 4 => m/n = 3/4 ___(1)

n : o = 8 : 9 => n/o = 8/9 ____(2)

find. m : o

Solution :

from eq(1),

m/n = (3/4) x (2/2) = 6/8 ____(3)

Multiplying eq(3) and eq(2) ,

⇒ (m/n) x (n/o)

⇒ (6/8) x (8/9)

⇒ (6/9)

⇒ ⅔

FINAL ANSWER :

$\tt \ast \: the \: \: value \: \: of \: \: \: \boxed{ \rm m : o = 2 : 3}$