Question

If 0.1% of m is equal to 10% of n, then m is what percent of 10n?

Answer 1

Hint: The concept of percentages will be used in this question. To convert percentages into fractions or decimals, we have to divide the percentage by 100. For example, 40% is equal to 0.4.


Complete step-by-step answer:
It is given that 0.1% of m is equal to 10% of n, so we can write that
0.1% of m = 10% of n
Converting the percentages into fractions according to the given formula we get-
$\dfrac{0.1}{100}\times\mathrm m=\dfrac{10}{100}\times\mathrm n$
Cancelling 100 in the denominator on both sides-
0.1m = 10n
m = 100n …(1)

Now, let m be x% of 10n, so we can write that
$\dfrac{\mathrm x}{100}\times10\mathrm n=\mathrm m$
Using equation (1), m = 100n so
$\dfrac{\mathrm x}{100}\times10\mathrm n=100\mathrm n$
The n in the numerator gets cancelled, hence we can find x as-
x = 1000%

So, m is 1000% of 10n. This is the required answer.

Note:In this question, it is important to read and understand the language in the question necessary. Each word is important. Just form the equations and assume the variables according to what is askes in the question. One should always keep in mind that whenever the percentage is given, we need to divide it by hundred to convert it into fraction or decimal form.