Can't find the correct solution for this one. Any help?

fambrini wrote:The price of a left-handed widget increased 20% in 1981 and 10% in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

A) 40%
B) 35%
C) 30%
D) 26%
E) 24%

OA: E

Let the original price = 100.
After a 20% increase, the 1981 price = 100 + (20% of 100) = 100+20 = 120.
After a 10% increase, the 1982 price = 120 + (10% of 120) = 120+12 = 132.
By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?
Percent decrease from 132 to 100 = (difference)/(larger) * 100 = (32/132) * 100 = (8/33) * 100 = 8 * (100/33) ≈ 8 * 3 = 24.

The correct answer is E.

fambrini wrote:The price of a left-handed widget increased 20% in 1981 and 10% in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

A) 40%
B) 35%
C) 30%
D) 26%
E) 24%

OA: E

We can let the pre-1981 price of the widget = x.

Thus, after a 20% increase in price, in 1981, the new price is 1.2x.

After a 10% increase in price, in 1982, the new price is 1.1(1.2x) = 1.32x.

We need to determine by approximately what percentage would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price. We can create the following equation in which n = the percentage decrease.

(1.32x)(1 - n/100) = x

(1.32x)[(100-n)/100] = x

We can convert 1.32 to a fraction and cancel out the x’s, so we have:

(132/100)[(100-n)/100] = 1

(100-n)/100 = 100/132

Cross-multiplying gives us:

132(100 - n) = 10,000

13,200 - 132n = 10,000

132n = 3200

n = 3200/132 ≈ 24

Answer:E

The easiest way for me:

x * (1.2) * (1.1) * (something) = x

x * (6/5) * (11/10) * (something) = x

Divide both sides by x:

6/5 * 11/10 * something = 1

Something = 1/(6/5 * 11/10)

Something = 1/(66/50) = 50/66 = 25/33

So we'd have to multiply by 25/33 to get back to the original price. 25/33 = 1 - 8/33, so our price would decrease by 8/33, or 24/99, or ≈ 24%.