Question

15 2 1 1 36 Solve : — + = = 17, -+-- = — хух у 5

JEE/Engineering Exams

Maths

Solution

117

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Sol. We have the equations: ( frac{15}{x}+frac{2}{y}=17 ) and [ frac{1}{x}+frac{1}{y}=frac{36}{5} ] ( frac{2}{x}+frac{2}{y}=frac{72}{5} ) 11 Multiplying eq. (ii) by ( 2, ) we get, Subtracting (iii) from (i), we get [ begin{array}{l} frac{15}{x}-frac{2}{y}=17-frac{72}{5} Rightarrow frac{13}{x}=frac{85-72}{5} Rightarrow frac{13}{x}=frac{13}{5} Rightarrow quad x times 13=13 times 5 quad Rightarrow x=frac{13 times 5}{13}=5 end{array} ] Putting the value of ( x ) in (ii), we get [ frac{1}{5}+frac{1}{y}=frac{36}{5} Rightarrow frac{1}{y}=frac{36}{5}-frac{1}{5} Rightarrow frac{1}{y}=frac{35}{5} Rightarrow 35 times y=5 Rightarrow y=frac{5}{35} quad therefore quad y=frac{1}{7} ] Hence, ( x=5, y=frac{1}{7} )