A sum of money is to be divided among Allan, Bill and Carol. Allan receives $\$ 1$ plus one-third of what is left. Bill then receives $\$ 6$ plus one-third of what remains. Carol receives the rest, which amounts to $\$ 40$. How much did Bill receive?
(A) $\$ 26$
(B) $\$ 28$
(C) $\$ 30$
(D) $\$ 32$
(E) $\$ 34$
A sum of money is to be divided among Allan, Bill and Carol. Allan receives $\$ 1$ plus one-third of what is left. Bill then receives $\$ 6$ plus one-third of what remains. Carol receives the rest, which amounts to $\$ 40$. How much did Bill receive?
(A) $\$ 26$
(B) $\$ 28$
(C) $\$ 30$
(D) $\$ 32$
(E) $\$ 34$

## Solution

After Allan had received his share, Bill received $\$ 6$ plus one-third of the remainder.

Since Carol gets the rest, she received two-thirds of the remainder, which is $\$ 40$.

Thus, one-third of the remainder is $\$ 20$.

The amount Bill receives is $\$ 26$.

ANSWER: (A)