Question
Download Solution PDFA started a work and left working after 9 days now B finished the remaining work in 24 days. Had A left the work after working for 13 days then B would have finished the remaining work in next 18 days. Then find in how many days A and B together can complete the work
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A worked for 9 days, B finished the remaining work in 24 days.
A worked for 13 days, B finished the remaining work in 18 days.
Formula used:
Work = Rate × Time
Calculation:
Let 'a' be the fraction of work A does in one day, and 'b' be the fraction of work B does in one day.
From the given information:
9a + 24b = 1 (whole work) ---- (1)
And, 13a + 18b = 1 (whole work) -- (2)
Multiply Equation 1 by 13 and Equation 2 by 9:
117a + 312b = 13
117a + 162b = 9
Subtract the second equation from the first:
150b = 4
b = 4/150 = 2/75
Substitute b = 2/75 into Equation 1:
9a + 24(2/75) = 1
9a = 1 - 48/75
9a = 27/75
a = 3/75 = 1/25
A's rate of work is 1/25 of the work per day.
B's rate of work is 2/75 of the work per day.
Combined rate of A and B
⇒ a + b = 1/25 + 2/75 = 3/75 + 2/75 = 5/75 = 1/15
If A and B work together, they complete 1/15 of the work in one day.
Let 'd' be the number of days A and B take together to complete the work.
(1/15) × d = 1
d = 15
∴ A and B together can complete the work in 15 days.
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