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Five technicians of a Studio A can do a work in 30 days. Eight technicians of a Studio B can do the same work in 15 days. In how many days can one technician of Studio A and one technician of Studio B, together do the same work?

Five technicians of a Studio A can do a work in 30 days. Eight technicians of a Studio B can do the same work in 15 days. In how many days can one technician of Studio A and one technician of Studio B, together do the same work? Correct Answer <span class="math-tex">\(\frac{{200}}{3}\)</span>

Number of technicians × studio A × days = Number of technicians × studio B × days

⇒ 5 × studio A × 30 = 8 × studio B × 15

⇒ 5 × studio A = 4 × studio B

⇒ Studio A/Studio B = 4/5

⇒ Time taken by one technician of studio A and one technician of studio B together to complete the work = (5 × 4 × 30)/(4 + 5)

⇒ Time taken by one technician of studio A and one technician of studio B together to complete the work = 200/3 days

∴ Total work will be done by one technician of studio A and one technician of studio B together in 200/3 days.

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