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QA – Placement Quizzes | Work and Wages | Question 13

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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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Last Updated : 28 Jun, 2021
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