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1. 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 :

A. $9 \frac{1}{3}$ days

B. 11 days

C. $12 \frac{1}{4}$ days

D. $16 \frac{1}{3}$ days

Solution:

\begin{aligned} (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 \\ 7 x and 4 x respectively \\ Then, 7 x + 4 x = \frac{1}{7} \\ \Rightarrow 11 x = \frac{1}{7} \\ \Rightarrow x = \frac{1}{77} \\ ∴ A's 1 day's work \\ = \frac{1}{77} \times 7 = \frac{1}{11} \end{aligned}

So, A will do the work in 11 days

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