Multiple choice

To complete a piece of work, Samir takes 6 days and Tanvir takes 8 days alonerespectively. Samir and Tanvir took Rs.2400 to do this work. When Amir joined them,the work was done in 3 days. What amount was paid to Amir?

  1. Rs. 300

  2. Rs. 400

  3. Rs. 800

  4. Rs. 500

  5. Rs. 100
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A Correct answer
Explanation

Samir's rate is 1/6 and Tanvir's is 1/8. Together with Amir, they complete the work in 3 days, so their combined rate is 1/3. Amir's rate is 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24. Amir's share of the 2400 is (1/24) / (1/3) * 2400 = (1/8) * 2400 = 300.

AI explanation

Using the LCM method, let the total work be 24 units, making the daily work rates of Samir and Tanvir 4 units and 3 units respectively. When Amir joins them, their combined rate is 24 / 3 = 8 units per day, so Amir's daily work rate is 8 - 4 - 3 = 1 unit. Amir works for 3 days to complete 3 units of the total 24 units, so his share of the Rs. 2400 payment is (3 / 24) * 2400 = Rs. 300.

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