QA – Placement Quizzes | Work and Wages | Question 13

Two friends A and B were hired to paint a room. A alone can paint the room in 10 days and is twice as efficient as B. Due to lack of resources, they decided to work alternatively with A starting first. Find the days it will take to paint the room.
(A) 13
(B) 15
(C) 16
(D) 18

Answer: (A)
Explanation: We are given that A alone can paint the room in 10 days and A is twice as efficient as B.
=> B alone would take double the time than A alone ,i.e., 20 days.
Now, let the total work of painting be LCM (10, 20) = 20 units.
=> Efficiency of A = 20/10 = 2 units / day
=> Efficiency of B = 20/20 = 1 unit / day
Since they work alternatively with A starting first, room painted in 1 cycle of 2 days = 3 units
=> Room painted in 6 cycles (total 12 days) = 18 units
Now, we are left with 20-18 = 2 units of painting and it is A’s turn to paint, who can paint 2 units in a day.
Therefore, total number of days required to paint the room = 12 + 1 = 13
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