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?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e.
LCM(16,12) = 48 units of work
Raj’s 1-day work = 48/16 = 3 units/day
Suraj’s 1-day work = 48/12 = 4 units/day
(Raj starts first, then Suraj next day)
In 2 days = 3(Raj) + 4(Suraj)=7 units
48 ÷ 7 = 6 full cycles ⇒ 6 × 2 = 12 days
Total work done in 6 cycles = 6 × 7 = 42 units
Remaining work = 48 − 42 = 6 units
Day 13: Raj → 3 units (total so far: 45)
He only needs 3 more units, and Suraj does 4 units/day:
Time taken on Day 14 = 3/4 day
Total days = 13 + 3/4 = days