Let the Rate of A = RA & the Rate of B = RB

2RA + 9RB = 1..............1

3RA + 6RB = 1..............2

equation 1 & 2

2RA + 9RB = 3RA + 6RB.............RA = 3RB

From 3 in 1

6RB + 9RB = 1.........15RB =1...........RB = 1/15..........Time taken by B alone = 15 days

RA= 3 * 1/15 = 1/5..........Time taken by A alone = 5 days

Answer: A

P.S.: Many ways to solve 2 equation with 2 unknowns. I chose to find relationship between RA & RB less time for me than solving 2 equations simultaneously.

rate * time = work
let A is the rate of worker A, and B is the rate of worker B.

given:
2A + 9B = 3A + 6B
3B = A , B = A/3

to find A days:
2A + 9B = 2A + 9(A/3) = 2A + 3A = 5A; i.e: with rate of A, 5 days are needed to finish the work.

to find B days:
2A + 9B = 2(3B) + 9B = 6B + 9B = 15B; i.e: with rate of B, 15 days are needed to finish the work.

so A.
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A started a work and left after working for 2 days. Then B did the remaining work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them working alone, finish the whole work?

A. A = 5 days and B = 15 days
B. A = 7 days and B = 21 days
C. A = 8 days and B = 18 days
D. A = 4 days and B = 12 days
E. A = 15 days and B = 15 days

let a=a's time to finish work alone
b=b's time to finish work alone
2/a+9/b=1
3/a+6/b=1
adding two equations,
5/a+15/b=2
plugging in choice A,
5/5+15/15=2 works
A=5 days and B=15 days
A