Correct Answer - Option 1 : 12
Given:
A can do a work in 21 days.
B is 50% more efficient than A.
C is twice efficient than B.
A started the work alone and worked for some days and left the work.
Then B and C joined together and finished the work in 2 days.
Formula Used:
If A and B can together finish a work in t days and alone can finish the work in a and b days respectively,
Then, 1/a + 1/b = 1/t
Work = Time × Efficiency
Calculation:
Time required by B = 2/3 × 21 = 14 days
C will take 7 days (As C is twice efficient than B)
Let total work be = LCM of 21, 14, 7 = 42 units and let A worked for x days alone.
Efficiency of A = 2
Efficiency of B = 3
Efficiency of A = 6
ATQ,
⇒ 2x + 9 × 2 = 42
⇒ 2x = 24
⇒ X = 12 days
∴ A works for 12 days alone.