Question

If a:b=5:8 and b:c=81:25. Find
a:c

Answer 1

Q. If A : B = 5 : 8 and B : C = 81 : 25, find A : C.

Solution :

A : B = 5 : 8 and B : C = 81 : 25

⇒ $\frac{A}{B} =\frac{5}{8}$ and $\frac{B}{C} = \frac{81}{25}$

⇒ $(\frac{A}{B} \times\frac{B}{C}) = (\frac{5}{8} \times\frac{81}{25})$

⇒ $\frac{A}{C} = \frac{81}{40}$

⇒ A : C = 81 : 40

Hence, A : C = 81 : 40.

Answer 2

Hey there !

Solution:

Given:

• a : b = 5 : 8
• b : c = 81 : 25

To Find:

• a : c = ?

Proof:

a : b = 5 : 8

$\implies \frac{a}{b} = \frac{5}{8} \\ \\ \implies b = \frac{8a}{5}$

Substituting the value of b in ( b:c ) we get,

$\implies \frac{b}{c} = \frac{81}{25} \\ \\ \implies \frac{8a}{5} \times \frac{1}{c} = \frac{81}{25} \\ \\ \implies \frac{8a}{5c} = \frac{81}{25} \\ \\ Cross \ multiplying \ terms \ we \ get, \\ \\ \implies \frac{a}{c} = \frac{ 81 \times 5}{25 \times 8} \\ \\ \implies \frac{a}{c} = \frac{405}{200} \\ \\ \implies \frac{a}{c} = \frac{81}{40} \\ \\ \boxed{ Hence \ a : c = 81 : 40 }$

Hope my answer helped !