Question

What percent of 42 is 29.4?

Answer 1

Hint: We here have been given the number 42 and asked what percentage of 42 is 29.4. For this, we will assume the percentage to be x%. Then we will use the formula given as follows:
Any percentage, ‘P%’ of any number N, is given as:
$$R=N\times {\displaystyle \frac{P}{100}}$$
Where R is the resultant percent of N.
After that, we will put all the given values in this formula as a result of which we will get an equation in terms of ‘x’. Then, we will solve that equation and hence get our answer.

Complete step by step answer:
Here, we have been given the number and we have been asked what percent of this number, i.e. 42 is 29.4.
Now, let us assume that the required percentage is ‘x%’.
Hence, x percent of 42 is equal to 29.4.
Now, we know that when we have been given a principal number, let us assume it to be ‘N’, any percent of that number, let us assume that percentage to be ‘P%’, is given as:
$$R=N\times {\displaystyle \frac{P}{100}}$$ …..(i)
Where R is the resultant percent of N.
Now, according to this question, we have:
N=42
P=x
R=29.4
Now, if we put all these values of N, P and R in equation (i), we can get an equation in terms of ‘x’ and we can solve it for ‘x’, hence obtain its value.
Hence, putting the values of N,P and R in equation (i) we get:
$$\begin{array}{rl}& R=N\times {\displaystyle \frac{P}{100}}\\ & \Rightarrow 29.4=42\times {\displaystyle \frac{x}{100}}\end{array}$$
Now, solving this equation to obtain the value of ‘x’, we get:
$\begin{array}{rl}& 29.4=42\times {\displaystyle \frac{x}{100}}\\ & \Rightarrow \left(29.4\right)\left(100\right)=42x\\ & \Rightarrow 2940=42x\\ & \Rightarrow x={\displaystyle \frac{2940}{42}}\\ & \therefore x=70\end{array}$

Hence, the required percentage is 70%.

Note: We have here used the formula $$R=N\times {\displaystyle \frac{P}{100}}$$. This is obtained as follows:
Now, the meaning of percentage is the amount of something in each ${100}^{th}$ of its part. Hence, if we have been given P of a number N is R, it means that R is the ${{\displaystyle \frac{P}{100}}}^{th}$ fraction of that number.
Hence, we get:
$$R=N\times {\displaystyle \frac{P}{100}}$$