A can do a work in 12 days and B can do the same work in 18 days. If they work on it together for 4 days, then what fraction of the work is left?

Correct option is A

Given:

A completes the work in 12 days

B completes the work in 18 days

Both work together for 4 days

Find: Fraction of work left

Method required: LCM method

Formula Used:

Work rate = Total work ÷ time

Work done = (Rate of A + Rate of B) × Time worked

Solution:

Total work = LCM(12, 18) = 36 units

A’s 1-day work = $$\frac{36}{12}$$ = 3 units

B’s 1-day work = $$\frac{36}{18}$$ = 2 units

Combined 1-day work = 3 + 2 = 5 units

Work done in 4 days = 5 × 4 = 20 units

Work left = 36 − 20 = 16 units

Fraction of work left = $$\frac{16}{36}$$​ = $$\frac49$$​​