Multiple choice

Ajay and Vijay undertake to do a piece of work for Rs 200. Ajay alone can do it in 24 days while Vijay alone can do it in 30 days. With the help of Pradeep, they finish the work in 12 days. How much should Pradeep get for his work?

  1. Rs 20

  2. Rs 100

  3. Rs 180

  4. Rs 50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ajay's rate is 1/24, Vijay's is 1/30. Together they do 1/24 + 1/30 = 5/120 + 4/120 = 9/120 = 3/40 per day. With Pradeep, they do 1/12 per day. Pradeep's contribution is 1/12 - 3/40 = 10/120 - 9/120 = 1/120 per day. In 12 days, Pradeep does 12 * 1/120 = 1/10 of the work. His share is 1/10 * 200 = 20.

AI explanation

Ajay's daily work rate is 1/24 of the job and Vijay's is 1/30, so together their rate is 3/40 of the job per day. Since they finish the job in 12 days with Pradeep, their combined rate with Pradeep is 1/12, meaning Pradeep's daily work is 1/12 minus 3/40, which equals 1/60. Ajay and Vijay's combined effort over the 12 days accounts for 36/40 of the total job, which is 9/10 of the work. Therefore, Pradeep only completed 1/10 of the total work, so out of the total Rs 200 paid, he should receive Rs 20.

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