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Three workers A, B and C together can complete the work in 5 days. Worker A is 25% more efficient than B and C takes 8 days more than A to complete the work when working alone. If worker D can complete the task in 24 days working with A, how many days it will take for both of them to complete the work?1. 6 days2. 8 days3. 16 days4. 4 days5. 5 days |
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Answer» Correct Answer - Option 2 : 8 days Worker A is 25% more efficient than B and C takes 8 days more than A to complete the work ∴ Let the time taken by B to complete the work be x days Then, time taken by A = x × (100/125) = 4x/5 Time taken by C = (4x/5) + 8 = 4(x + 10)/5 Together can complete the work in 5 days ∴ (1/x) + (5/4x) + (5/4x + 40) = 1/5 ⇒ {4(x + 10) + 5(x + 10) + 5x}/4x(x + 10) = 1/5 ⇒ (14x + 90)/(4x2 + 40x) = 1/5 ⇒ 70x + 450 = 4x2 + 40x ⇒ 4x2 – 30x – 450 = 0 ⇒ 2x2 – 15x – 225 = 0 ⇒ 2x2 – 30x + 15x – 225 = 0 ⇒ 2x(x – 15) + 15(x – 15) = 0 ⇒ x = 15, -15/2 Rejecting negative value of x Time taken by A = (4 × 15)/5 = 12 days Time taken by D = 24 days ∴ Working together ⇒ (1/12) + (1/24) = (2 + 1)/24 = 1/8 ∴ Time taken by both of them is 8 days |
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