Question

Two numbers are respectively \[20\%\] and \[50\%\] more than the third number. What \[\\%\] is the first number of the second number?
1. \[40\%\]
2. \[50\%\]
3. \[80\%\]
4. \[70\%\]

Answer 1

Hint: Two numbers are respectively \[20\%\] and \[50\%\] more than the third number. What \[\%\] is the first number of the second number?
We are requested to get the percentage, so we will convert them to fractions so that we can multiply them by 100 to get percentages. Taking the first number as a starting point, make increments in the first two numbers, and then multiply the percentages from the ratio by 100 to get the result in percentages.

Complete step-by-step solution:
Considering the third number be x
Then, first number \[=120\%\,\,\text{of}\,\,x\]
\[=\dfrac{120x}{100}\]
By reducing the fraction in term of x we get:
\[=\dfrac{6x}{5}\]
Now we have to find the second number that is
Second number \[=150\%\,\,\text{of}\,\,x\]
By converting the percentages into ratio we have to divide by 100 we get:
\[=\dfrac{150x}{100}\]
By reducing the fraction in term of x we get:
\[=\dfrac{3x}{2}\]
Now we have the ratio of first two number that is
\[\dfrac{\text{first number}}{\text{second}\,\,\text{number}}=\dfrac{\left( \dfrac{6x}{5} \right)}{\left( \dfrac{3x}{2} \right)}\]
Here, x get cancelled from both numerator as well as denominator we get
\[\dfrac{\text{first number}}{\text{second}\,\,\text{number}}=\dfrac{\left( \dfrac{6}{5} \right)}{\left( \dfrac{3}{2} \right)}\]
By simplifying further and further solving we get:
\[\dfrac{\text{first number}}{\text{second}\,\,\text{number}}=\dfrac{12}{15}\]
By simplifying further and reducing the fraction we get:
\[\dfrac{\text{first number}}{\text{second}\,\,\text{number}}=\dfrac{4}{5}\]
Remember that to convert any fraction into percentages we have to multiply by 100 we get;
\[\dfrac{\text{first number}}{\text{second}\,\,\text{number}}=\dfrac{4}{5}\times 100\%\]
So after simplification we get:
\[\dfrac{\text{first number}}{\text{second}\,\,\text{number}}=\dfrac{400}{5}\%\]
Further solving this we get:
\[\dfrac{\text{first number}}{\text{second}\,\,\text{number}}=80\%\]
So, the correct option is “option 3”.

Note: To answer problems like these, you'll need to know how percentages are calculated, how to make increments and decrements in them, and, most significantly, how to convert percentages to fractions and vice versa.