If Sharon's weekly salary increased by 16 percent, she would earn $406 per week. If instead, her weekly salary were to increase by 10 percent, how much would she earn per week?

(A) $374.
(B) $382.
(C) $385.
(D) $392.
(E) $399.

The OA is C.

I did manage to find a way to solve this particular problem in time, but I really want to know how an expert works through these calculations, as they won't always be encountered in a percent situation or the answer choices may be too near.

Experts, can you assist me with this PS question please? Thanks!

Hi LUANDATO,
Let's take a look at your question.

Let Sharon's weekly salary be 'x'.
If her salary is increased by 16%, she would earn $406 per week.
This can be represented as:
$$x+x\left(16\%\right)=406$$
$$x+x\left(\frac{16}{100}\right)=406$$
$$x+x\left(0.16\right)=406$$
$$x\left(1+0.16\right)=406$$
$$1.16x=406$$
$$x=\frac{406}{1.16}$$
$$x=\frac{406\times100}{116}$$
$$x=350$$

The weekly salary of Sharon is $350.

In the next sentence, the question states that If instead, her weekly salary were to increase by 10 percent, how much would she earn per week?
Let's first find 10% increase in he weekly salary.

$$=350\times\left(10\%\right)$$
$$=350\times\left(\frac{10}{100}\right)$$
$$=35$$

Therefore the total weekly salary after 10% increase will be = 350 + 35 = $385

Hence, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.

LUANDATO wrote:If Sharon's weekly salary increased by 16 percent, she would earn $406 per week. If instead, her weekly salary were to increase by 10 percent, how much would she earn per week?

(A) $374.
(B) $382.
(C) $385.
(D) $392.
(E) $399.

Test an EASY CASE.
Let the salary = 100.
Increased by 10%, the salary = 100 + 10 = 110.
Increased by 16%, the salary = 100 + 16 = 116.
Resulting ratio:
110/116 = 55/58, implying that the salary increased by 10% is equal to 55/58 of the salary increased by 16%.

Since Sharon's salary increased by 16% = 406, we get:
Sharon's salary increased by 10% = (55/58) * 406 = 55 * 7 = 385.

The correct answer is C.

Consider the salary being equal to = 100.

Increase in salary by 16% implies --> 100 + (100*0.16) = 116
Increase in salary by 10% implies --> 100 + (100*0.10) = 110

The resulting ratio = 110/116 = 55/58
This implies that salary increase by 10% is equivalent to 55/58 of a salary increase by 16%

Since Sharon's salary increased by 16% = 406, we get:
Sharon's salary increased by 10% = (55/58) * 406 = 55 * 7 = 385.