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**Hint**: In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction. 35. 100.

**Complete step-by-step answer**:

We need to first understand the requirement of the question which is by how much percent is Ram’s income more than rajan’s .

Let us assume Ram’s income is $ Rs100 $ .

According to the question we have been given that Rajan earns $ 33\dfrac{1}{3}\% $ less than Ram.

So we can write $ 100 - 33\dfrac{1}{3}\% $ . By breaking the terms we have $ 100 - \dfrac{{100}}{3} $ .

It gives us a value $ 100 - 33.33 = 66.67 $ . So we have the difference of income i.e. $ 100 - 66.67 = 33.33 $ .

Now we will divide Ram’s income by Rajan’s income to get the result, i.e. $ \dfrac{{33.33}}{{66.67}} $ .

We have to find the value in percent so we can write $ \dfrac{{33.33}}{{66.67}} \times 100 \Rightarrow 49.99 $ , by approximating the value we have $ 50\% $ .

Hence the correct option is (B) $ 50\% $ .

**So, the correct answer is “Option B”.**

**Note**: We should always be careful what the question is asking. Based on the requirement and by observing all the necessary information that is already available in the question we gather the information and then create an equation or by unitary method whichever is applicable, then we solve the problem and then verify the answer by putting the value in the problem and see whether we get the same answer or not.

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