Multiple choice

Aditi can finish a software development project in 30 days if she works 8 hours a day, while Kavya can finish the same project in 16 days working 10 hours a day. They agree to collaborate under the condition that Kavya will work twice as many hours per day as Aditi, and Aditi will work twice as many days as Kavya. If Aditi works 4 hours a day, determine the number of days Kavya will work.

  1. 14

  2. 15

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Aditi's total required time is 240 hours, and Kavya's is 160 hours, meaning their hourly work rates are 1/240 and 1/160 of the project, respectively. Under the collaboration terms, if Aditi works 4 hours a day for 2D days, and Kavya works 8 hours a day for D days, the sum of their work is (8D / 240) + (8D / 160) = 1. Solving this equation gives D = 12 days for Kavya.

AI explanation

Aditi's total hours to complete the project are 30 days times 8 hours, equaling 240 hours, while Kavya's total hours are 16 days times 10 hours, equaling 160 hours. Since Aditi works 4 hours a day and Kavya works twice as many, Kavya works 8 hours a day; since Aditi works twice as many days as Kavya, if Kavya works for D days, Aditi works for 2D days. Their combined work is Aditi's 8D hours divided by 240 plus Kavya's 8D hours divided by 160, which sets up the equation D/30 + D/20 = 1. Solving this gives 5D divided by 60 equals 1, meaning Kavya works for 12 days.

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