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If a/b=2/3 and b/c=4/5,then find value of a+b/b+c. |
| Answer» Mehod 1:-\xa0In 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\xa0{tex}{a\\over b} ={2\\over 3}{/tex}\xa0and\xa0{tex}{b\\over c}={4\\over 5}{/tex}{tex}=> a={2\\over 3}b{/tex}\xa0and\xa0{tex}{c\\over b}={5\\over 4}{/tex}\xa0{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\xa0{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\xa0{tex}{a\\over b}={2\\over 3}{/tex}\xa0and\xa0{tex}{b\\over c}={4\\over 5}{/tex}Now\xa0{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] | |