Question

Reena types 600 words in four minutes. How much time will she take to type 3,150 words?

Answer 1

Hint: We use the concept of unitary method to find the time taken by Reena to type the required number of pages. We first find the time taken to type 1 word using unitary method and then again use unitary method to find the time required to type a given number of words.

Complete step by step solution:
We are given in the statement of question that Reena types 600 words in 4 minutes.
\[ \Rightarrow \]We are given the number of words typed \[ = 600\]
Since, Reena takes 4 minutes to type 600 words,
So the time taken\[ = 4\] minutes
We know unitary methods help us to find the value of a single unit when we are given the value of multiple units by dividing the value of multiple units by number of units.
\[ \Rightarrow \]Time taken to type 1 word \[ = \]Total time taken\[/\]number of words typed
Substitute the value of time taken as 4 and number of words as 600
\[ \Rightarrow \]Time taken to type 1 word\[ = \dfrac{4}{{600}}\]
Cancel same factors from numerator and denominator of RHS
\[ \Rightarrow \]Time taken to type 1 word\[ = \dfrac{1}{{150}}\]
\[ \Rightarrow \]Time taken by Reena to type 1 word is\[ = \dfrac{1}{{150}}\]minutes………….… (1)
Now we have to calculate time taken by Reena to type 3,150 words.
Use unitary method
\[ \Rightarrow \]Time taken to type 3,150 words \[ = \]Time taken to type 1 word\[ \times \]number of words required to type
Substitute the value from equation (1)
\[ \Rightarrow \]Time taken to type 3,150 words\[ = \left( {\dfrac{1}{{150}} \times 3150} \right)\]minutes
Cancel same factors from numerator and denominator of RHS
\[ \Rightarrow \]Time taken to type 3,150 words\[ = 21\] minutes

\[\therefore \]Time taken to type 3,150 words is 21 minutes.

Note: * Unitary method helps us to find the value of a single unit when we are given the value of multiple units by dividing the value of multiple units by the number of units given.
* Unitary method helps us to find the value of multiple units when we are given the value of a single unit by multiplying the value of a single unit by the number of units given.
Students many times make mistakes when they have to cancel factors from numerator and denominator, in case where the denominator is small we can either divide the numerator by denominator or write the numerator as a factor of denominator and other factors so we can cancel the same factors easily. Always write the unit of time as given in the question along with the final answer.