If a/b=2/3 and b/c=4/5,then find value …

Mehod 1:- In this method first of all we find value of a and  c from given equations in variable b. After that we find a+b and b+c and then divide them.

Given {tex}{a\over b} ={2\over 3}{/tex} and {tex}{b\over c}={4\over 5}{/tex}

     {tex}=> a={2\over 3}b{/tex} and {tex}{c\over b}={5\over 4}{/tex} {tex}=> c={5\over 4}b{/tex}

Now a+b={tex}{2b\over 3}+b={2b+3b\over 3}={5b\over 3}{/tex}

and b+c={tex}b+{5b\over 4}={4b+5b\over 4}={9b\over 4}{/tex}

So {tex}{a+b\over b+c}={{5b\over 3}\over {9b\over 4}}={5b\over 3}×{4\over 9b}{/tex}={tex}{20\over27}{/tex}

Method 2:-

Given {tex}{a\over b}={2\over 3}{/tex} and {tex}{b\over c}={4\over 5}{/tex}

Now {tex}{a+b\over b+c}={{a+b\over b}\over {b+c\over b}}{/tex}        [on dividing numerator and denominator by b]

                  ={tex}{{a\over b}+{b\over b}}\over{{b\over b} +{c\over b}}{/tex}={tex}{{a\over b}}+1\over{1+{c\over b}}{/tex}={tex}{{2\over 3}}+1\over {1+{5\over4}}{/tex}={tex}{2+3\over 3}\over {4+5\over 4}{/tex}={tex}{5\over 3}\over {9\over 4}{/tex}={tex}{5\over 3}×{4\over 9}{/tex}={tex}20\over 27{/tex}   [by substituting the values of a/b and c/b]