Question Number 6906 by Tawakalitu. last updated on 02/Aug/16
Commented by Rasheed Soomro last updated on 02/Aug/16
![Let there are x students in Class C There will be x+4 students in Class B [4 more than C] and x+8 in Class A.[4 more than B] Let every student of Class A gets y sweats Every student of Class B will get y+3 sweats[3 more than A] and every student of Class C y+8 sweats[5 more than B] −−−−−−−−−−−−−−−−−−−−−−−−−−− A B C No. of sudents x+8 x+4 x No. of sweats/each y y+3 y+8 Total sweats/Class (x+8)y (x+4)(y+3) x(y+8) Difference of sweats of Classes A and B=10 (x+8)y−(x+4)(y+3)=10 xy+8y−xy−3x−4y−12=10 −3x+4y=22...........................(i) Difference of sweats of Classes B and C=14 (x+4)(y+3)−x(y+8)=14 xy+3x+4y+12−xy−8x=14 −5x+4y=2.............................(ii) By (i)−(ii) 2x=20 Or x=10 Substituting x=10 in (i) or (ii) we will get y=13 So finally, −−−−−−−−−−−−−−−−−−−−−−−−−−− A B C No. of sudents 18 14 10 No. of sweats/each 13 16 21 Total sweats/Class 234 224 210 Grand total of sweats of all the three Classes=668](Q6909.png)
$${Let}\:{there}\:{are}\:{x}\:{students}\:{in}\:{Class}\:{C} \\ $$$${There}\:{will}\:{be}\:{x}+\mathrm{4}\:{students}\:{in}\:{Class}\:{B}\:\left[\mathrm{4}\:{more}\:{than}\:{C}\right] \\ $$$$\:\:\:\:\:\:\:{and}\:\:{x}+\mathrm{8}\:{in}\:{Class}\:{A}.\left[\mathrm{4}\:{more}\:{than}\:{B}\right] \\ $$$$ \\ $$$${Let}\:{every}\:{student}\:{of}\:{Class}\:{A}\:{gets}\:\:{y}\:\:{sweats} \\ $$$${Every}\:{student}\:{of}\:{Class}\:{B}\:{will}\:{get}\:\:{y}+\mathrm{3}\:{sweats}\left[\mathrm{3}\:{more}\:{than}\:{A}\right] \\ $$$$\:\:\:\:\:\:{and}\:\:{every}\:{student}\:{of}\:{Class}\:{C}\:\:{y}+\mathrm{8}\:\:{sweats}\left[\mathrm{5}\:{more}\:{than}\:{B}\right] \\ $$$$−−−−−−−−−−−−−−−−−−−−−−−−−−− \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{A}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{B}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{C} \\ $$$${No}.\:{of}\:{sudents}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}+\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}+\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x} \\ $$$${No}.\:{of}\:{sweats}/{each}\:\:\:\:\:\:\:\:\:\:\:{y}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}+\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}+\mathrm{8} \\ $$$${Total}\:{sweats}/{Class}\:\:\:\:\:\left({x}+\mathrm{8}\right){y}\:\:\:\:\:\left({x}+\mathrm{4}\right)\left({y}+\mathrm{3}\right)\:\:\:\:\:\:{x}\left({y}+\mathrm{8}\right) \\ $$$$ \\ $$$$\:\:\:{Difference}\:{of}\:{sweats}\:{of}\:{Classes}\:{A}\:\:{and}\:\:{B}=\mathrm{10} \\ $$$$\:\:\:\:\:\left({x}+\mathrm{8}\right){y}−\left({x}+\mathrm{4}\right)\left({y}+\mathrm{3}\right)=\mathrm{10} \\ $$$$\:\:\:\:\:\:{xy}+\mathrm{8}{y}−{xy}−\mathrm{3}{x}−\mathrm{4}{y}−\mathrm{12}=\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{22}...........................\left({i}\right) \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:{Difference}\:{of}\:{sweats}\:{of}\:{Classes}\:{B}\:\:{and}\:\:{C}=\mathrm{14} \\ $$$$\:\:\:\:\:\:\:\:\:\:\left({x}+\mathrm{4}\right)\left({y}+\mathrm{3}\right)−{x}\left({y}+\mathrm{8}\right)=\mathrm{14} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{xy}+\mathrm{3}{x}+\mathrm{4}{y}+\mathrm{12}−{xy}−\mathrm{8}{x}=\mathrm{14} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{5}{x}+\mathrm{4}{y}=\mathrm{2}.............................\left({ii}\right) \\ $$$$\:\:\:\:{By}\:\:\left({i}\right)−\left({ii}\right)\:\:\:\:\:\mathrm{2}{x}=\mathrm{20} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Or}\:\:{x}=\mathrm{10} \\ $$$$\:\:\:\:{Substituting}\:{x}=\mathrm{10}\:{in}\:\left({i}\right)\:{or}\:\left({ii}\right)\:{we}\:{will}\:{get} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}=\mathrm{13}\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${So}\:{finally}, \\ $$$$−−−−−−−−−−−−−−−−−−−−−−−−−−− \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{A}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{B}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{C} \\ $$$${No}.\:{of}\:{sudents}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{18}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{14}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{10} \\ $$$${No}.\:{of}\:{sweats}/{each}\:\:\:\:\:\:\:\mathrm{13}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{16}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{21} \\ $$$${Total}\:{sweats}/{Class}\:\:\:\:\:\:\mathrm{234}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{224}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{210} \\ $$$${Grand}\:{total}\:{of}\:{sweats}\:{of}\:{all}\:{the}\:{three}\:{Classes}=\mathrm{668} \\ $$
Commented by Tawakalitu. last updated on 02/Aug/16
$${Wow}\:..\:{great}..\:{i}\:{really}\:{appreciate} \\ $$