Multiple choice

Priya can lay tiles on a large floor in 36 days, while Karan can complete the same task in 54 days. Priya starts working alone and lays tiles for 12 days. After that, Karan and Meera join her, and the three of them complete the remaining work in 12 more days. If the total payment for laying the tiles is Rs. 45,000, what is Meera's share of the money, assuming it is distributed in proportion to the amount of work done by each person?

  1. Rs. 3,800

  2. Rs. 3,200

  3. Rs. 4,000

  4. Rs. 5,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Priya rate = 1/36, Karan rate = 1/54. Priya works 12 days = 12/36 = 1/3 work. Remaining = 2/3. In 12 days, Priya + Karan + Meera do 2/3 work. Rate (P+K+M) = (2/3)/12 = 1/18. Meera rate = 1/18 - (1/36 + 1/54) = 1/18 - 5/108 = 6/108 - 5/108 = 1/108. Work done by Meera = 12 * (1/108) = 1/9. Share = (1/9) * 45,000 = 5,000.

AI explanation

Taking the least common multiple of 36 and 54, the total work is 108 units. Priya works alone for 12 days, completing 12 times 3, or 36 units, leaving 72 units of work. In the next 12 days, Priya, Karan, and Meera complete the remaining 72 units, meaning their combined hourly rate is 72 divided by 12, which is 6 units per day. Since Priya completes 3 units daily and Karan completes 2 units daily, Meera's daily work is 6 minus 5, equaling 1 unit. Meera's total work is 12 units, so her share of the total 108 units is 12 divided by 108, meaning she receives one-ninth of Rs. 45,000. Meera's share is Rs. 5,000.

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