Brain and Austin can paint 720 boxes in 20 days . Austin and David in 24 days…
2025
Brain and Austin can paint 720 boxes in 20 days . Austin and David in 24 days and David and Brain in 15 days . Brain works for 6 days , Austin for 10 days and Davis for 8 days . The total number of boxes painted by them is?
- A.
420
- B.
500
- C.
670
- D.
550
Attempted by 426 students.
Show answer & explanation
Correct answer: A
Answer: 420
Let the number of boxes painted per day by Brian, Austin and David be B, A and D respectively.
From Brian and Austin: B + A = 720 / 20 = 36
From Austin and David: A + D = 720 / 24 = 30
From David and Brian: D + B = 720 / 15 = 48
Solve these three equations to find individual rates:
B = ( (B+A) + (B+D) - (A+D) ) / 2 = (36 + 48 - 30) / 2 = 27
A = ( (B+A) + (A+D) - (B+D) ) / 2 = (36 + 30 - 48) / 2 = 9
D = ( (B+D) + (A+D) - (B+A) ) / 2 = (48 + 30 - 36) / 2 = 21
Compute the total boxes painted when Brian works 6 days, Austin 10 days and David 8 days:
Total = 6×B + 10×A + 8×D = 6×27 + 10×9 + 8×21 = 162 + 90 + 168 = 420.