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Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of \(x\)?
Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of \(x\)?
A. \(1\) B. \(1.25\) C. \(2\) D. \(2.5\) E. \(4\)
After 2 hours \(2*\frac{1}{10}=\frac{1}{5}\) of the taks will be done (as only A works);
After 4 hours \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task will be done and \(\frac{1}{5}\) will be left to be done;
We are told that 1/5th of the task is done in 15 minutes (1/4th of an hour) by all three workers: \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\). From which we can find that \(x=2\) hours.
Consider the total work as 10, and A can do 1 work in 1hr, B can do 2 work in 1 hr. A starts work for 2 hrs. So 2 work completed(1×2=2), then B joins for 2 hrs, so B does 4 work (2×2=4), now total work = A's 4+B's 4 work = 8. Balance work is 2. C joins and complete the work in 15 mins. That is A do .25 work and B do .5 work in15 mins., total .75 work(.25+.5=.75).Balace 1.25 work is done by C in 15 mins. So C can do 5 work in 1 hr. It means C takes 2hrs to complete the total work. Ans : opt.c, 2hrs
A - 10 hours to complete the work B- 5 hours to complete the work C- X hours to complete the work Take the LCM of 10,5,x = 10x (total work) Hence A rate of work = 10x/10 = X units/hour B rate of work = 10x/5 = 2x units/hour C rate of work = 10x/x = 10 units/hour therefore X*2 +(2x+x)*2+(2x+x+10)*1/4 =10x this gives X =2 (quick and easy)
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67% (02:13) correct 
