raj can build a house alone in 16 days but suraj alone can build it in 12 days. raj and suraj work on alternate days. if raj works on first day the house will be built in how many days?
Answers
Raj can build the house in 16 days
1 day = 1/16 of the house
Suraj can build the house in 12 days
1 day = 1/12 of the house
Find the work done in every 2 days (Raj on the first day and Suraj on the second)
2 days = 1/16 + 1/12 = 7/48
Find the number of 2 days needed:
7/48 of the works = 2 days
Number of 2 days = 48 ÷ 7 = 6
Find the number of days:
Total number of days = 6 x 2 = 12
Find the remaining work after 12 days:
Remaining work = 1 - (7/48 x 6) = 1/8 of the work
On the 13th day:
13th day, Raj will complete 1/16 of the work
Work remaining = 1/8 - 1/16 = 1/16
On the 14th day:
14th day, Suraj will complete 1/12 of the work
Work remaining = 1/12 - 1/16 = -1/48 of the work
Day not needed = 1/48 x 12 = 1/4
Day worked = 1 - 1/4 = 3/4
⇒ Work was completed with 13 3/4 days
Answer: They will need 13 3/4 days
In 1 day Raj does 1/16 amount of work.
In 1 day Suraj does 1/12 amount of work
First Day Raj works and Second Day Suraj.
So in 2 days work done = 1/16+1/12 = 7/48 amount of work
So in 12 days, (i.e. 6 times 2 days) work done =
6x7/48 = 7/8
Remaining work =1/8
Now on 13th day Raj will work and complete 1/12 amount of work
1/12>1/16
Find out how much is 1/16th of 1/12th
Here is the fraction
5/7 of 1/12
= 5/7x1/12 = 5/84
¾ of 1/12
= 3/4x 1/12 = 1/16
That means Raj completes the remaining work in 3/4th day
So the answer is 13+3/4 = 13/3/4 days