Question

A and B working separately can finish a work in 15 days and 20 days. respectively. If they work on alternate days. A starting first, and if the work goes on for 8 days, what part of the work will be left unfinished?

• A. 7/60
• B. 3/5
• C. 8/15
• D. 1/4

Answer 1

Answer:

C. 8/15

Solution: Given: Time taken by A to complete work = 15 days Time taken by B to complete work = 20 days Alternate work goes on for 8 days Formula used: Total work = Time taken × Efficiency Calculation: Let the total work be x So, A's one-day work = x/15 And B's one-day work = x/20 Work done in 8 days working alternate = (x/15 + x/20) × 4 ⇒ [(4x + 3x)/60] × 4 ⇒ 28x/60 Work remaining = x - (28x/60) ⇒ (60x - 28x)/60 ⇒ 32x/60 The unfinished part = 32/60 = 8/15 of total work Hence, 8/15 part of the work will be left unfinished. Shortcut Trick Let the total work = LCM of 15 and 20 Total work = 60 units A's efficiency = 60/15 = 4 units/day B's efficiency = 60/20 = 3 units/day 8 days alternate work = 4 days working together Work completed in 4 days working together = 4 × (4 + 3) ⇒ 7 × 4 = 28 units Remaining work = 60 - 28 = 32 units Part of work left unfinished = 32/60 = 8/15 Hence, 8/15 part of the work will be left unfinished.