Question

If 20% of 10% of a number is 12, what is 10% of 20% of the same number?

Answer 1

12

Explanation:

Long Answer:

"20% of 10% of a number is 12" translates to:

.2 (times) .1 (times) x = 12

of translated to times.

20%=.20 or .2

10%=.10 or .1

number translated to variable.

is translated to equals.

We have the following equation to solve:

`.2 \cdot .1 \cdot x=12`

Simplifying the .2 times .1 part:

`.02 \cdot x=12`

Divide both sides by .02:

`x=(12)/(.02)`

`x=600`

Now it ask for "what is 10% of 20% of the same number?"

Multiplication is communicative and I wouldn't have done all of this work if I had seen them just switch the 10% and 20% around. The answer is 12.

But for fun since we already done all of this work!

"10% of 20% of 600" translates to:

.1 (times) .2 (times) 600

`.1 \cdot .2 \cdot 600`

`.02 \cdot 600`

`12`.

Short Answer:

.2(.1)x=12 so .1(.2)x=12

Multiplication is commutative is the reason the answer is 12.

Answer 2

There are 5 20% in 100% ( 20 x 5 = 100)

So 10% of a number would be 12 x 5 = 60

Then there are 10 10% in 100% ( 10 x 10 = 100).

So if 10% = 60, then 100% = 60 x 10 = 600.

The starting value is 600

600 x 10% = 600 x 0.1 = 60

60 x 20% = 60 x 0.2 = 12

Now you have the starting value you can calculate the other answer:

600 x 20% = 600 x 0.20 = 120

120 x 10% = 120 x 0.10 = 12

The answer would be 12