A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone ?
A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone ?
A2 : 5
B2 : 7
C3 : 7
D1 : 5
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Answer is 1 : 5
Explanation:
(A + B)’s 1 day’s work = \(\frac{1}{20}\)
(B + C)’s 1 day’s work = \(\frac{1}{30}\)
(C + A)’s 1 day’s work = \(\frac{1}{40}\)
On adding,2(A + B + C)’s 1 day’s work
= \(\frac{1}{20}+\frac{1}{30}+\frac{1}{40}\)
= \(\frac{6+4+3}{120}\) = \(\frac{13}{120}\)
(A + B + C)’s 1 day’s work= \(\frac{13}{240}\)
A’s 1 day’s work
= \(\frac{13}{240}-\frac{1}{30}\)= \(\frac{13-8}{240}\)
= \(\frac{5}{240}= \frac{1}{48}\)
C’s 1 day’s work
= \(\frac{13}{240}-\frac{1}{20}= \frac{13-12}{240} = \frac{1}{240}\)
Required ratio = 48 : 240 = 1 : 5
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