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If machine A and B can produce 1100 units in 9 h and 12 h respectively. In how many hours can machine A and B working together at these constant rates
Question

If machine A and B can produce 1100 units in 9 h and 12 h respectively. In how many hours can machine A and B working together at these constant rates produce 1100 units?

A.

367\frac{36}7​​

B.

377\frac{37}7​​

C.

397\frac{39}7​​

D.

387\frac{38}7​​

Correct option is A

Given:
Machine A produces 1100 units in 9 hours.​​
Machine B produces 1100 units in 12 hours.

Formula Used:

Time=Total WorkCombined Rate\text{Time} = \frac{\text{Total Work}}{\text{Combined Rate}}

Solution:

​Work rate of machine A  = 11009\frac{1100 }{9 }​ = 122.22 units/hour

Work rate of machine B = 110012\frac{1100}{12}​ = 91.67 units/hour

Combined work rate = 122.22 + 91.67  = 213.89 units/hour

Time = 1100213.89 \frac{1100}{213.89 } ​= 367 \frac{36}{7}​ hours

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