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Two taps running together can fill a tank in 31 hours. If one tap takes3 hours more than the other to fill the tank, then how much time wileach tap take to fill the tank? |
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Answer» Let the smaller diameter tap takes x hours to fill the tank Then, time taken by larger diameter tap to fill the tank=(x-3) Both taps together can fill the tank in 40/13 hours portion of tank filled by smaller diameter tap in x hours= 1/x portion of tank filled by smaller diameter tap in40/13 hours= 40/13x portion of tank filled bylarger diameter tap in (x-3) hours=1/x-3 portion of tank filled bylarger diameter tap in 40/13 hours= 40/13(x-3) ATQ,40/13x+40/13(x-3)=1 1/x+1/x-3=13/40 x-3+x/x(x-3)=13/402x-3/x²-3x=13/40 13x-119x+120=0a=13b=119c=120D=b²-4ac =14161-6240 =7921applying quadratic formula we get two roots = -b+√D/2a and -b-√D/2a119+89/26 and 119-89/268 and 15/13x= 15/13 neglected because time taken by smaller tap cannot be less than 3 hours so smaller tap time = 8 hours and larger tap = 5 hours |
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