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Ram alone can finish a task in 20 days while Shyam alone can finish it in 30 days. How many days will they take to finish the task if they work togeth
Question

Ram alone can finish a task in 20 days while Shyam alone can finish it in 30 days. How many days will they take to finish the task if they work together?

A.

18

B.

16

C.

12

D.

14

Correct option is C

Given:
Ram can complete the task in 20 days.
Shyam can complete the task in 30 days.
Formula Used:
Combined Work Rate=1Time taken by Ram+1Time taken by ShyamTotal Time=1Combined Work Rate\text{Combined Work Rate} = \frac{1}{\text{Time taken by Ram}} + \frac{1}{\text{Time taken by Shyam}}\\\text{Total Time} = \frac{1}{\text{Combined Work Rate}}​​
Solution:
Combined Work Rate = 120+130=360+260=560=112\frac{1}{20} + \frac{1}{30} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12}

Total Time=1112=12 days\text{Total Time} = \frac{1}{\frac{1}{12}} = 12 \, \text{days}

Alternate Solution:

Total Work = LCM of 20 and 30 = 60 unit
Efficiency of Ram = 6020\frac{60}{20} ​= 3 unit per day
Efficiency of Shyam = 6030\frac{60}{30} ​ = 2 unit per day

Total Time=Total WorkCombined Efficiency=602+3=12 days\text{Total Time} = \frac{\text{Total Work}}{\text{Combined Efficiency}} = \frac{60}{2+3} = 12 \, \text{days}

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