Question

Ram’s income is \[20\% \] less than Shyam’s. How much is Shyam’s income more than Ram’s in percentage terms?
A.\[20\% \]
B.\[25\% \]
C.\[30\% \]
D.\[15\% \]

Answer 1

Hint: Here, we will assume Shyam’s income to be \[x\]. Using the given information, we will find Ram’s income in terms of \[x\]. We will find the difference in the incomes of Ram and Shyam. Then we will divide it by Ram’s income and multiply this by 100 to find the required percentage.

Complete step-by-step answer:
Let the income of Shyam be \[x\].
Now it is given that Ram’s income is \[20\% \] less than Shyam’s.
Hence, we can write this as:
Ram’s Income \[ = x - \dfrac{{20}}{{100}}x\]
Simplifying the fraction, we get
\[ \Rightarrow \] Ram’s Income \[ = x - \dfrac{x}{5} = \dfrac{{5x - x}}{5}\]
Subtracting the terms in the numerator, we get
\[ \Rightarrow \] Ram’s Income \[ = \dfrac{{4x}}{5}\]
Now, we are required to find how much is Shyam’s income more than Ram’s in percentage terms.
Hence, we will find the difference between Shyam’s income and Ram’s income.
Difference between income \[ = x - \dfrac{{4x}}{5}\]
Taking LCM, we get
\[ \Rightarrow \] Difference between income \[ = \dfrac{{5x - 4x}}{5}\]
Subtracting the terms in the numerator, we get
\[ \Rightarrow \] Difference between income \[ = \dfrac{x}{5}\]
Therefore, the required percentage will be: \[\dfrac{{\dfrac{x}{5}}}{{\dfrac{{4x}}{5}}} \times 100\]
This is because, in order to convert a fraction into percentage, we multiply it by 100.
Hence, the required percentage \[ = \dfrac{x}{{4x}} \times 100 = \dfrac{1}{4} \times 100 = 25\% \]
Therefore, Shyam’s income is \[25\% \] more than Ram’s in percentage terms.
Hence, option B is the correct answer.

Note:An alternate way of solving this question is:
Let the income of Shyam be \[100\].
We know that Ram’s income is \[20\% \] less than Shyam’s.
Hence, we can write this as:
Ram’s Income \[ = 100 - \dfrac{{20}}{{100}} \times 100\]
Simplifying the expression, we get
\[ \Rightarrow \] Ram’s Income \[ = \left( {100 - 20} \right)\]
Subtracting the terms, we get
\[ \Rightarrow \] Ram’s Income \[ = 80\]
Now, we are required to find how much is Shyam’s income more than Ram’s in percentage terms.
Hence, we will take the difference between Shyam’s income and Ram’s income as our numerator, i.e. \[\left( {100 - 80} \right) = 20\]
And, since we are required to compare this with Ram’s income, hence, we will take his income as the denominator, i.e. \[80\]
Therefore, the required percentage will be: \[\dfrac{{20}}{{80}} \times 100\]
This is because, in order to convert a fraction into a percentage, we multiply it by 100.
Hence, the required percentage \[ = \dfrac{{20}}{{80}} \times 100 = \dfrac{1}{4} \times 100 = 25\% \]
Therefore, Shyam’s income is \[25\% \] more than Ram’s in percentage terms.
Hence, option B is the correct answer.
We can use either of the two ways to solve this question.