Question

Anil takes 6 days less than the time taken by Varun to finish a piece of work. If both Anil and Varun together can finish that work in 4 days, find the time taken by Varun to finish the work independently.

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Answer 1

Let the time taken by Varun to finish a piece of work be x days.

Then the time taken by Anil to complete the same work = x - 6

Time taken if they work together = 4 days

Thus, we have

begin mathsize 18px style 1 over x plus fraction numerator 1 over denominator x minus 6 end fraction equals 1 fourth fraction numerator x minus 6 plus x over denominator x left parenthesis x minus 6 right parenthesis end fraction equals 1 fourth fraction numerator 2 x minus 6 over denominator x squared minus 6 x end fraction equals 1 fourth 8 x minus 24 equals x squared minus 6 x x squared minus 6 x minus 8 x plus 24 equals 0 x squared minus 14 x plus 24 equals 0 x squared minus 12 x minus 2 x plus 24 equals 0 x left parenthesis x minus 12 right parenthesis minus 2 left parenthesis x minus 12 right parenthesis equals 0 left parenthesis x minus 12 right parenthesis left parenthesis x minus 2 right parenthesis equals 0 x equals 12 space space o r space space x equals 2 end style

Now, x = 2 is rejected since x - 6 = 2 - 6 = -4 which cannot be number of days.

Hence, x = 12

Hence, time taken by Varun to complete the work independently is 12 days.