Mathematics
Grade6
Easy
Question
A machine takes 3 minutes to prepare 6 fabrics, then ___________ fabrics are prepared in 1 hour.
- 100
- 120
- 105
- 115
Hint:
In this question, we are given the time taken by machine to make 6 fabrics. It is 3 minutes. We have to find the number of fabrics that a machine can make in 1 hour, given that the rate is constant. We can try to find an equation using these quantities and find the given value.
The correct answer is: 120
The machine requires 3 minutes to make 6 fabrics.
Let the number of fabrics be denoted by ‘N’.
N = 6
Time = 3 minutes.
We have to find the number of fabrics made in 1 hour. For that, we have to find the rate. We can find a rate by taking the ratio of the number of fabrics and the time required. The rate is constant.
Let’s see the formula.
![R a t e space equals fraction numerator N over denominator T i m e end fraction
S u b s t i t u t i n g space t h e space v a l u e s.
R a t e space equals space fraction numerator 6 space f a b r i c s over denominator 3 space m i n u t e s end fraction
space space space space space space space space space equals space 2 space f a b r i c s space p e r space m i n u t 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![R a t e space equals fraction numerator N over denominator T i m e end fraction](data:image/png;base64,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)
Now, we have to find the number of fabrics made in 1 hour. We have found the rate in fabric per minute. So, we to make the units same. We will have to convert 1 hour into minutes. 1 hour is 60 minutes.
So the given time is
Time = 1 × 60 minutes
= 60 minutes
Let’s find the number of fabrics made in 60 minutes.
We will rearrange this equation for ‘N’. We will multiply both sides by time.
N = rate × time
N = 2 × 60
N = 120
Therefore, the machine makes 120 fabrics in 1 hour.
We have to be careful about the units. Same quantities must have same units. If necessary we need to convert units.