Problem Solving

Richard receives an increment in his salary. His salary presently forms 30% of the total income of his family. Before the increment his salary used to form 20% of the total income of his family. By how many percentage points did the salary of Richard as a percentage of his family's total income increase?

A) 14(2/7)
B) 16(2/3)
C) 10
D) 8
E) 13(3/7)

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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

Let 'x' be the total family income then,
Before the increment Richard's salary = (20%)(x) = 0.2 x
After increment Richard's salary = (30%)(x) = 0.3 x

The percentage points of the salary of Richard as a percentage of his family's total income increase can be calculated as,
$$=\frac{\left(0.3x-0.2x\right)}{x}\times100\%$$
$$=\frac{0.1x}{x}\times100\%$$
$$=0.1\times100\%=10\%$$

It can also be calculated as 30%-20% = 10%

Therefore, Option C is correct,

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