Multiple choice

Ram and Sandhu took a contract to do a work together for Rs. 600. Ram alone is able to complete it in 16 days and Sandhu alone is able to complete it in 24 days. If Sunita helps them, they can finish the work in 8 days only. How much money will Ram get when Sunita helps?

  1. Rs. 200

  2. Rs. 300

  3. Rs. 100

  4. Rs. 400

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: Ram = 1/16, Sandhu = 1/24. Together = 1/16 + 1/24 = 5/48. With Sunita, rate = 1/8. Sunita's rate = 1/8 - 5/48 = 1/48. Total work is shared in ratio of rates: 1/16 : 1/24 : 1/48 = 6 : 4 : 2 = 3 : 2 : 1. Ram's share = (3/6) * 600 = 300.

AI explanation

When Sunita helps them, the payment should still be distributed based on the proportion of work Ram and Sandhu actually did during those 8 days. Let the total work be the least common multiple of 16 and 24, which is 48 units; Ram's efficiency is 3 units per day and Sandhu's is 2 units per day. In 8 days, Ram completes 3 times 8 equaling 24 units of work, and Sandhu completes 2 times 8 equaling 16 units of work. Ram's share of the total Rs. 600 is his 24 units divided by the combined 40 units completed by him and Sandhu, resulting in a fraction of 3 over 5. Multiplying Rs. 600 by 3 over 5 gives Rs. 300, meaning Ram gets Rs. 300.

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