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17 trainees can do as much work as 4 experts can do in a day. It takes 12 experts and 9 trainees 5 days to dig a pond. How many trainees will one need alongside 4 experts to dig a similar pool in 15 days?

17 trainees can do as much work as 4 experts can do in a day. It takes 12 experts and 9 trainees 5 days to dig a pond. How many trainees will one need alongside 4 experts to dig a similar pool in 15 days? Correct Answer 3

Let, a trainee’s efficiency = x/day

An expert’s efficiency = y/day

According to the question,

⇒ 17x = 4y

⇒ x = 4y/17      ----(1)

According to the question,

⇒ 5(9x + 12y) = 1

⇒ 5(36y/17 + 12y) = 1

⇒ (36y + 204y) × 5/17 = 1

⇒ 1200y = 17

⇒ y = 17/1200

∴ x = 4/17 × 17/1200 = 4/300

Let, number of trainees required = k

According to the question,

⇒ 15 × = 1

⇒ 17/20 + k/20 = 1

⇒ k + 17 = 20

⇒ k = 3

∴ 3 trainees will be needed

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