Multiple choice

Rancho alone can complete a job in 18 days. Farhan alone can complete the same job in 30 days. Rancho, Farhan and Raju together complete the job in 9 days and get paid a total of Rs. 2000 for it. Find Rancho's share (in Rs.).

  1. 500

  2. 1000

  3. 600

  4. 400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rancho's rate = 1/18, Farhan's rate = 1/30. Together (R+F+Raju) = 1/9. Raju's rate = 1/9 - 1/18 - 1/30 = (10-5-3)/90 = 2/90 = 1/45. Ratio of work done = 1/18 : 1/30 : 1/45 = 5:3:2. Total parts = 10. Rancho's share = (5/10) * 2000 = 1000.

AI explanation

Since Rancho and Farhan finish the job in 18 and 30 days, their combined daily work is 1/18 + 1/30 = 8/90. All three finish the work in 9 days, so their combined work is 1/9 or 10/90. Subtracting Rancho and Farhan's contribution from the total, Raju's daily work is 10/90 - 8/90 = 2/90 = 1/45. The Rs. 2000 payment is divided in the ratio of their daily work: 1/18 : 1/30 : 1/45. Multiplying by 90 gives the ratio 5 : 3 : 2. Rancho's share is 5/10 of the total Rs. 2000, which equals Rs. 1000.

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