A and B can do a piece of work in 45 days and 40 days respectively. Th...
According to the question,
(A + B)'s 1 day work = 1/45 + 1/40 = 17/360
(A + B)'s 'n' day work = 17n/360
Now, the remaining work i.e. 1 - 17n/360 is completed by 'B' in (n + 14) days.
Thus,
(n + 14)/40 = 1 - 17n/360
=> 9(n + 14) = 360 - 17n
=> 9n + 126 = 360 - 17n
=> 26n = 234
=> n = 9.
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A and B can do a piece of work in 45 days and 40 days respectively. Th...
Understanding the Work Rates
A's work rate: A can complete the work in 45 days, thus A's work rate is 1/45.
B's work rate: B can complete the work in 40 days, thus B's work rate is 1/40.
Combined Work Rate
When A and B work together, their combined work rate is:
(1/45) + (1/40)
To find a common denominator (which is 360), we can calculate:
- A's work in 1 day = 8/360
- B's work in 1 day = 9/360
Combined work rate = (8 + 9) / 360 = 17/360
Work Done in n Days
In 'n' days, the amount of work completed by A and B together is:
Work done = n * (17/360)
Remaining Work After A Leaves
After 'n' days, A leaves, and B finishes the remaining work in "n + 14" days. The work done by B in that time is:
Work done by B = (n + 14) * (1/40)
Setting Up the Equation
Total work = Work done in 'n' days + Work done by B
Thus, we can equate:
n * (17/360) + (n + 14) * (1/40) = 1
Solving the Equation
To solve for 'n', we convert the equation into a single equation and find 'n':
1. Multiply through by 720 (LCM of 360 and 40) to eliminate fractions.
2. Simplify and solve for 'n'.
After solving, we find that n = 9.
Conclusion
A left after 9 days, confirming option 'C' as the correct answer.
A and B can do a piece of work in 45 days and 40 days respectively. Th...
Answer ( C ) 9 days