Question
Download Solution PDFA can do a work in 20 days and B in 30 days. If they work on it together for 2 days, then what is the fraction of the work that is left?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A can do a work in 20 days.
B can do a work in 30 days.
They work together for 2 days.
Concept Used:
When two or more individuals work together, their combined work rate is the sum of their individual work rates.
Formula Used:
Work rate of A = 1/20 work/day
Work rate of B = 1/30 work/day
Combined work rate = (1/20 + 1/30) work/day
Fraction of work done = Combined work rate × Number of days they work together
Fraction of work left = 1 - Fraction of work done
Calculation:
Combined work rate = 1/20 + 1/30
⇒ Combined work rate = 3/60 + 2/60
⇒ Combined work rate = 5/60 = 1/12 work/day
Fraction of work done in 2 days = (1/12) × 2
⇒ Fraction of work done = 1/6
Fraction of work left = 1 - 1/6
⇒ Fraction of work left = 6/6 - 1/6
⇒ Fraction of work left = 5/6
∴ The fraction of the work that is left is 5/6.
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