Question Number 40271 by Rio Mike last updated on 18/Jul/18
$${Using}\:{Bionomial}\:{solve}; \\ $$$${Given}\:{that}\:\:{y}\:=\:\mathrm{3}{x}\:\:{and}\:{x}\:{increases} \\ $$$${at}\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\%,\:{find}\:\:{percentage}\:{increase} \\ $$$${in}\:{y}. \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 19/Jul/18
$${y}=\mathrm{3}{x}\:\:\:{dy}=\mathrm{3}{dx} \\ $$$${given}\:\frac{{dx}}{{x}}×\mathrm{100}=\frac{\mathrm{5}}{\mathrm{2}} \\ $$$$\frac{{dy}}{{y}}×\mathrm{100} \\ $$$$=\frac{\mathrm{3}{dx}}{\mathrm{3}{x}}×\mathrm{100} \\ $$$$=\frac{\mathrm{5}}{\mathrm{2}} \\ $$$${or}... \\ $$$${let}\:{initial}\:{value}\:{of}\:{x}=\mathrm{100} \\ $$$${inigial}\:{value}\:{of}\:{y}=\mathrm{300} \\ $$$${x}+\bigtriangleup{x}=\mathrm{100}+\frac{\mathrm{5}}{\mathrm{2}}=\frac{\mathrm{205}}{\mathrm{2}} \\ $$$${y}+\bigtriangleup{y}=\mathrm{3}×\frac{\mathrm{205}}{\mathrm{2}}=\frac{\mathrm{615}}{\mathrm{2}} \\ $$$$\bigtriangleup{y}=\frac{\mathrm{615}}{\mathrm{2}}−\mathrm{300}=\frac{\mathrm{15}}{\mathrm{2}} \\ $$$${percentage}\:{y}\:{increase}=\frac{\mathrm{15}}{\mathrm{2}×\mathrm{300}}×\mathrm{100}=\frac{\mathrm{5}}{\mathrm{2}} \\ $$$${pls}\:{check}... \\ $$$$ \\ $$