Anil is twice as good a student as Bharat and is able to finish a work in 30 minutes less than Bharat’s time. Find the time in which both of them can finish the same work together?
Given Anil is twice as good a student as Bharat
$$\Rightarrow$$ Efficiency of Anil : Efficiency of Bharat = 2:1
and also, Efficiency is inversely proportional to Time taken,
$$\Rightarrow$$ Time taken by Anil : Time taken by Bharat = 1:2...............................(1)
Given that Time taken by Anil is 30 min less than Bharat's time.
Let say, Time taken by Bharat be 't' minutes.
Then the time taken by Anil = t-30 minutes
Substituting these in equation (1), we get
$$\frac{t-30}{t} = \frac{1}{2}$$
$$\Rightarrow$$ t = 60 minutes.
Therefore the time taken by Anil and Bharat are 30 minutes and 60 minutes respectively.
Let Efficiency of Bharat be 'x', then Efficiency of Anil will be '2x'
$$\Rightarrow$$ Total Work = Efficiency\times Time taken = $$(2x)\times 30 (or) (x)\times 60 = 60x$$ units.
Efficiency when Anil and Bharat are working together = x+2x = 3x
Total Work = 60x units
Time taken(T) by Anil and Bharat together to complete the work = Total work/ Efficiency when Anil and Bharat work together
$$\Rightarrow T = \frac{60x}{3x}$$
$$\Rightarrow$$ T = 20 minutes.
Create a FREE account and get: