Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts

[Vincen]

Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?

(A) $110
(B) $120
(C) $180
(D) $220
(E) $260

[spoiler]OA=D[/spoiler]

Source: Magoosh

[deloitte247]

Let total money in Al's account = a
Let total money in Eliot's account = e
$$a-e=\frac{1}{12}\left(a+e\right)$$
$$a-e=\frac{a+e}{12}$$
12a - 12e = a + e
12a - a = e + 12e
11a = 13e .............eqn 1

a increased by 10% => a + 10% of a
= a + 0.1a = 1.1a
e increased by 20% => e + 20% of e
= e + 0.2e = 1.2e
1.1a = 1.2e + $22
$$a=\frac{1.2e+22}{1.1}.............eqn\ 2$$
Substitute eqn 2 in eqn 1
$$11a=13a\ where\ a=\frac{1.2e+22}{1.1}$$
$$11\cdot\frac{\left(1.2e+22\right)}{1.1}=13e$$
$$\frac{13.2e+242}{1.1}=13e$$
$$13.2e\ +\ 242\ =\ 14.3e$$
$$14.3e-13.2e=242$$
$$\frac{1.1e}{1.1}=\frac{242}{1.1}$$
$$e=$220$$

Answer = D

[Scott@TargetTestPrep]

Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?

(A) $110
(B) $120
(C) $180
(D) $220
(E) $260

[spoiler]OA=D[/spoiler]

Source: Magoosh

We can create the equations:

A - E = 1/12(A + E)

12A - 12E = A + E

11A = 13E

and

1.1A = 1.2E + 22

11A = 12E + 220

Subtracting the second equation from the first,we have:

0 = E - 220

220 = E

Answer: D