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A and B can do a piece of work in 4 days and 46 days, respectively. The number of days [Correct to one decimal place] required to complete the work if
Question

A and B can do a piece of work in 4 days and 46 days, respectively. The number of days [Correct to one decimal place] required to complete the work if both A and B work together is:

A.

6.9

B.

5.5

C.

3.6

D.

6.8

Correct option is C

Given:

A can complete the work in 4 days.

B can complete the work in 46 days.

Formula Used:

Time = 1Rate of A+Rate of B\frac{1}{\text{Rate of A} + \text{Rate of B}}

Solution:

Rate of A = 14\frac{1}{4}​ (since A completes the work in 4 days)

Rate of B = 146\frac{1}{46}​ (since B completes the work in 46 days)

Time = Time=114+146\text{Time} = \frac{1}{\frac{1}{4} + \frac{1}{46}}

14+146=46+44×46=50184\frac{1}{4} + \frac{1}{46} = \frac{46 + 4}{4 \times 46} = \frac{50}{184}

Time = 150184=18450\frac{1}{\frac{50}{184}} = \frac{184}{50}​ = 3.68 days

Thus, 3.6 days 

Alternate Method: 

Total Work = 92 

Total Efficiency = 23+2 = 25 

Total time = 9225=3.6\frac{92}{25} = 3.6 Days ​

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