Quote:
Incorrect first solution that I posted earlier.
Option (A)
Let time to be found be \(X\), and let the work done to make one car be \(W\).
\(X* (\frac{W}{20} + \frac{W}{25}) = 10 W\)
Upon solving you get,
\(X\) = \(111\) \(\frac{1}{9}\) minutes.
New Correct solution:
Well this one got me too, and this is why I am keeping the original answer posted. I also missed the part of A and B working independently
not together. But, since they are not working together, my above solution is wrong.
Solution to the problem when both A and B are working independently is much easier, with almost no calculation required.
It's given that A can build a car in 20 mins, and B can build a car in 25 mins. So, Work rate of A is > that of B. So, if they work for similar no. of hours, A would make more than B does. Since, the #no. of cars is going to be an "
integer", we have to take the no. of minutes as the LCM of the (20, 25). That is 100 mins. So, for 100 mins, A would produce 5 cars (\(\frac{100}{20}=5\)), and B would produce 4 cars (\(\frac{100}{25}=4\)). So, that is 9 cars. Now the question asks us the time required to make 10 cars. Since, we have 9 out of 10 cars already, one car left would be made by A in lesser time than B. So, in another 20 minutes we will have one more car made by A. So, the total time taken to get 10 cars when both A and B are working independently is 100 + 20 mins =
120 mins.
\(Option (D).\)