The difference between 87% and 71% of a number is 448. What is 59% of that number

Question

Today I came across an objective type question in that I have to choose from 4 optiona. I found myself struggling with this question since I have not been in touch with Math since I completed my graduation.

The question was:

The difference between 87% and 71% of a number is 448. What is 59% of that number?

1562
1652
1662
1552

I would really appreciate any help on this.

Answer 1

With a reasoning from elementary school:

The difference is $16\,\%$ of that number. So, $1\,\%$ is $16$ times less, i.e. $\frac{448}{16}=28$, and $59\,\%$ is $59$ times the latter: $$59\times 28=1652.$$

Answer 2

As mentioned in the comments, $0.87x - 0.71x = 448$. Then you can use the unitary method:

$$0.16x=448$$ $$0.01x=28$$ $$0.59x = \ ?$$

Answer 3

Use the rule of three.

$448$ is for $16$
like $x$ is for 59

then:

$$\frac{59 \times 448}{16} = ?$$