Question
A takes 24 hours more than B to complete the work, and
32 hours more than C to complete the same work. The combined time taken by A and B to finish the work is equal to the time taken by C alone. Find the time required by B alone to complete the work.Solution
ATQ,
Let the time taken by C alone to complete the work be ‘x’ days. So, time taken by A alone to complete the work = (x + 32) days. Time taken by B alone to complete the work = (x + 32 – 24)= (x + 8) days According to question, {(x + 32) (x + 8)}/ {(x + 32) + (x + 8)} = x x ² + 40x + 256 = x(2x + 40) x ² = 256 x = 16 So, time taken by B alone to complete the work = 16 + 8 = 24 daysÂ
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