The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is

Options

1. 27
2. 35
3. 22
4. 16

Correct Answer

27

Explanation

Given: Kamal takes twice as long as Amal t_K = 2 * t_A So the AP is: t_A, t_S, 2 * t_A Therefore, the middle term: t_S = (t_A + 2 * t_A) / 2 = 3 * t_A / 2 Now work rates (work per day): Amal: r_A = 1 / t_A Sunil: r_S = 1 / t_S = 1 / (3 * t_A / 2) = 2 / (3 * t_A) = (2/3) * r_A Kamal: r_K = 1 / (2 * t_A) = (1/2) * r_A Given: Amal works 4 days, Sunil works 9 days, Kamal works 16 days and together they finish the whole job So: 4 * r_A + 9 * r_S + 16 * r_K = 1 job Substitute values: 4 * r_A + 9 * (2/3 * r_A) + 16 * (1/2 * r_A) = 1 4r_A + 6r_A + 8r_A = 18r_A = 1 So: r_A = 1/18 t_A = 18 days Sunil’s rate: r_S = (2/3) * (1/18) = 1/27 So Sunil’s time: t_S = 27 days Final Answer: 27 days

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