Question : A can do as much work in 4 days as B can do in 5 days and B can do as much work in 6 days as C in 7 days. In what time will C complete a piece of work that A can do in a week?
Option 1: $10\frac{5}{24}$ days
Option 2: $4\frac{4}{5}$ days
Option 3: $6\frac{8}{15}$ days
Option 4: $12\frac{6}{19}$ days
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Correct Answer: $10\frac{5}{24}$ days
Solution :
A's 4-day work = B's 5-day work
The ratio time is taken by A and B = 4 : 5
B's 6-day work = C's 7-day work
The ratio of time taken by B and C = 6 : 7
Combining the two ratios, we get:
The ratio of time taken by A, B and C,
A : B : C = 4 × 6 : 5 × 6 : 7 × 5 = 24 : 30 : 35
The ratio efficiency of A : B : C = $\frac{1}{24}:\frac{1}{30}:\frac{1}{35} = 35:28:24$
Let one day's work of A, B, and C be 35, 28 and 24 units.
7 days work of A = $7\times 35 = 245$ units
245 units completed by C = $\frac{245}{24}=10\frac{5}{24}$
Hence, the answer is $10\frac{5}{24}$ days.
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