Raj can build a house in 16 days by himself, while Suraj can do it in 12 days. Raj and Suraj work on alternate days. How many days would the house take to build if Raj starts working on the first day?
- A13
- B11
4
1
- C13
4
3
- D11
Solution & Step-by-step Explanation
Let the total work be the LCM of 16 and 12, which is 48 units.
Efficiency of Raj =
16
48
=3 units/day
Efficiency of Suraj =
12
48
=4 units/day
They work on alternate days, starting with Raj:
Day 1 (Raj): 3 units
Day 2 (Suraj): 4 units
Total work done in a 2-day cycle = 3+4=7 units.
Number of complete 2-day cycles to get close to 48 units:
6×7=42 units
This takes 6×2=12 days.
Remaining work = 48−42=6 units.
On Day 13, Raj works and completes his maximum capacity of 3 units.
Remaining work after Day 13 = 6−3=3 units.
On Day 14, it is Suraj's turn. He can complete 4 units in a full day. To complete the remaining 3 units, he will take:
Time=
4
3
day
Total time taken = 12+1+
4
3
=13
4
3
days.
Efficiency of Raj =
16
48
=3 units/day
Efficiency of Suraj =
12
48
=4 units/day
They work on alternate days, starting with Raj:
Day 1 (Raj): 3 units
Day 2 (Suraj): 4 units
Total work done in a 2-day cycle = 3+4=7 units.
Number of complete 2-day cycles to get close to 48 units:
6×7=42 units
This takes 6×2=12 days.
Remaining work = 48−42=6 units.
On Day 13, Raj works and completes his maximum capacity of 3 units.
Remaining work after Day 13 = 6−3=3 units.
On Day 14, it is Suraj's turn. He can complete 4 units in a full day. To complete the remaining 3 units, he will take:
Time=
4
3
day
Total time taken = 12+1+
4
3
=13
4
3
days.