Question

Ram and Shyam together can build a house in 10 days; Ram and Arun can build it together in 12 days and Shyam and Arun can build it in 15 days. Shyam, Arun and Ram start working together. In how many days they build the house?

• A. 4 days
• B. 6 days
• C. 8 days
• D. 12 days

Answer 1

Answer:

C. 8 days

Let R, S, and A be the fraction of the house Ram, Shyam, and Arun can build in one day, respectively. The given information translates to the following equations:

1. Ram and Shyam: R+S= 1/10​

2. Ram and Arun: R+A=​ 1/12

3. Shyam and Arun: S+A= 1/15​

Summing all three equations gives twice the combined rate:

2(R+S+A)= 1/10​ + 1/12​+ 1/15​

Find the Least Common Multiple (LCM) of 10,12, and 15, which is 60:

2(R+S+A) = 6/60​ + 5/60 ​+ 4/60​

2(R+S+A) = 6+5+4 ​/ 60=15 / 60​= 1/4​

Now, find the combined rate of all three:

R+S+A=1/4​×1/2​= 1/8​

The combined work rate is 1​/8 of the house per day.

3. Calculate the Time Taken

Since they complete 81​ of the work in one day, the total time taken to complete the entire house (i.e., 1 unit of work) is the reciprocal of the rate.

Time=Combined Rate1​=1/1​/8=8 days