Question

Find the value for $ 337\dfrac{1}{3}% $ of 696 days.
This question has multiple correct options
(a) 2349
(b) 2034
(c) 2348
(d) 2039

Answer 1

Hint: Here, first change the percentage from mixed fraction to an improper fraction or a normal fraction. Divide the fraction and substitute the given values in the general form of a percentage, Percentage = [(Obtained Value) / (Total value)] $ \times $ 100 and find the required value.

Complete step-by-step answer:
Here, in this question we need to find the value for $ 337\dfrac{1}{3}% $ of 696 days. In this, we need to use the principle of percentage.
Let us first change the percentage which is in the form of mixed numbers to an improper fraction.
 $ 337\dfrac{1}{3}=\dfrac{\left( 337\times 3 \right)+1}{3} $
Now, first multiply the numbers in the parentheses and then add the 1, we get
 $ 337\dfrac{1}{3}=\dfrac{1012}{3} $
Now, let us divide the number 1012 by 3 and write the value in the decimal form.
 $ 337\dfrac{1}{3}=337.33 $
Here, we have a percentage of 337.33%
We know, how to find the percentage,
Percentage = [(Obtained Value) / (Total value)] $ \times $ 100
If Obtained Value = $ x $ , Total value = $ T $ , we get
Percentage (%) = $ \dfrac{x}{T}\times 100 $
Now, from the given question we have values, Percentage (%) = 337.33%, Total Number of days = 696 days, therefore, let us find the obtained value or the required value $ \left( x \right) $ in this question.
 $ 337.33=\dfrac{x}{696}\times 100 $
Let us divide by 100 on both the sides of the equation, we get
 $ \begin{align}
  & \dfrac{337.33}{100}=\dfrac{x}{696}\times \dfrac{100}{100} \\
 & 3.3733=\dfrac{x}{696} \\
\end{align} $
Now, let us multiply by the number 696 on both the sides of the equation, we get
 $ 3.3733\times 696=\dfrac{x}{696}\times 696 $
Here, on the R.H.S. the 696 in the numerator and denominator gets cancelled out, we get the value of $ x $ .
 $ \begin{align}
  & x=2347.8168 \\
 & \approx 2348
\end{align} $
Hence, here the value will be approximately 2348 days and if leap year is considered it will be approximately 2349 days.

Note: Here, the leap year is considered as an assumption, and leap year has an extra day in the month of February, instead of 28 days in a leap year it has 29 days. Also, there is a short way to solve the mixed fractions or mixed numbers, just place a decimal right after the whole number given and divide the fraction next to it, the value we get is to be written beside the decimal we previously put after the given whole number.