Question

if a:b = 2:7, c:d = 2:1 and b:d = 5:4 then find a:c
​

Answer 1

$\textbf{Given:}$

$a:b=2:7$

$c:d=2:1$

$b:d=5:4$

$\textbf{To find:}$

$a:c$

$\textbf{Solution:}$

$\text{Consider,}$

$a:b=2:7$

$\implies\,a=2k\;\text{and}\;b=7k$

$c:d=2:1$

$\implies\,c=2m\;\text{and}\;d=m$

$b:d=5:4$

$\implies\dfrac{b}{d}=\dfrac{5}{4}$

$\implies\dfrac{7k}{m}=\dfrac{5}{4}$

$\implies\dfrac{k}{m}=\dfrac{5}{7{\times}4}$

$\implies\bf\dfrac{k}{m}=\dfrac{5}{28}$

$\text{Now,}$

$\dfrac{a}{c}$

$=\dfrac{2k}{2m}$

$=\dfrac{k}{m}$

$=\dfrac{5}{28}$

$\implies\dfrac{a}{c}=\dfrac{5}{28}$

$\implies\boxed{\bf\,a:c=5:28}$

Answer 2

Given: a : b = 2 : 7, c : d = 2 : 1, b : d = 5 : 4

To find: a : c

Solution:

• a : b = 2 : 7 or, a/b = 2/7

• c : d = 2 : 1 or, c/d = 2/1 or, d/c = 1/2

• b : d = 5 : 4 or, b/d = 5/4

• To find the ratio a : c, simply express a/c as a product of the given ratios.

• Now, a : c = a/c
• = a/b * b/d * d/c
• = 2/7 * 5/4 * 1/2
• = 10/56
• = 5/28 = 5 : 28
• Then a : c = 5 : 28

Answer: a : c = 5 : 28