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A can lay railway tracks between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days on
Question

A can lay railway tracks between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Considering this, C alone can do the job in:

A.

548\tfrac{5}{48} days​

B.

165\tfrac{16}{5}​ days

C.

48 days

D.

485\tfrac{48}{5}​ days

Correct option is D

Given:

A can complete the work in 16 days.

B can complete the work in 12 days.

A, B, and C together complete the work in 4 days.

Formula Used:

Work done per day=1Total days taken\text{Work done per day} = \frac{1}{\text{Total days taken}}​​

Efficiency of C=Total efficiency(Efficiency of A+Efficiency of B)\text{Efficiency of C} = \text{Total efficiency} - (\text{Efficiency of A} + \text{Efficiency of B})​​

Solution:

Work done by A in 1 day = 116\frac{1}{16}​​

Work done by B in 1 day =112 \frac{1}{12}​​

Work done by A, B, and C together in 1 day =14 \frac{1}{4}​​​

14=116+112+1C\frac{1}{4} = \frac{1}{16} + \frac{1}{12} + \frac{1}{C}​​

1C=14116112=123448=548\frac{1}{C} = \frac{1}{4} - \frac{1}{16} - \frac{1}{12} = \frac{12-3-4}{48}=\frac{5}{48}​​

C=485\frac{48}{5} days

Option (D) is right.

Alternate Method:

​Efficiency of C= 12 - 4 - 3 = 5

Time taken by C=485\frac{48}{5} days

Option (D) is right.​

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