A and B can do a job together in 7 days. A is \(1^{\frac{3}{4}}\) times as

Question

A and B can do a job together in 7 days. A is \(1^{\frac{3}{4}}\) times as efficient as B. The same job can be done by A alone in :

Options:

A . \(9\frac{1}{3}\)

B . 11 days

C . \( 12\frac{1}{4}\)

D . \(16\frac{1}{3}\)

Answer: Option B

(A's 1 day's work) : (B's 1 day's work) = \(\frac{7}{4}:1 = 7:4\)

Let A's and B's 1 day's work be 7x and 4x respectively.

Then, 7x + 4x = \(\frac{1}{7}\Rightarrow 11x =\frac{1}{7}\Rightarrow x=\frac{1}{77}\)

So, A's 1 day's work = \(\left(\frac{1}{77}\times7\right) = \frac{1}{11}\)

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