Question

What is the value of $x$ in: $45\% $ of $1500$ $ + $ $35\% $ of $1700$ $ = x\% $ of $3175$.
A. $30$
B. $35$
C. $40$
D. $50$

Answer 1

Hint: In the given question, we are required to find the value of x in the expression provided to us. The given expression provides a relation between certain percentages of numbers. We will calculate the percentages given to us in the left side of the equation and then find the value of x in the equation. Such questions require accuracy in arithmetic.

Complete step by step answer:
So, we are given that, $45\% $ of $1500$ $ + $ $35\% $ of $1700$ $ = x\% $ of $3175$.
Hence, we will calculate the value of percentages given to us in the left side of the equation.
So, we have to find $45\% $ of $1500$. So, let $45\% $ of $1500$ be $a$.
Then, \[a = 45\% \] of $1500$.
\[ \Rightarrow a = \dfrac{{45}}{{100}} \times 1500\]
Cancelling the common factors in the numerator and denominator of the fraction, we get,
\[ \Rightarrow a = 45 \times 15\]
\[ \Rightarrow a = 675\]
So, $45\% $ of $1500$ is $675$.
Now, we will calculate $35\% $ of $1700$.
Then, let $b = \;35\% $ of $1700$.
\[ \Rightarrow b = \dfrac{{35}}{{100}} \times 1700\]
Cancelling the common factors in the numerator and denominator of the fraction, we get,
\[ \Rightarrow b = 35 \times 17\]
\[ \Rightarrow b = 595\]
So, $35\% $ of $1700$ is $595$.

Now, substituting the values of these percentages in the given equation, we get,
$ \Rightarrow 675 + 595 = x\% $ of $3175$.
Adding up the terms, we get,
$ \Rightarrow 1270 = x\% $ of $3175$.
Now, we calculate x percent of the number $3175$ as $\dfrac{x}{{100}} \times 3175$. So, we get,
$ \Rightarrow 1270 = \dfrac{x}{{100}} \times 3175$
Now, transposing the terms, we get,
$ \Rightarrow x = \dfrac{{1270 \times 100}}{{3175}}$
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow x = 0.4 \times 100$
Multiplying the numbers, we get,
$ \Rightarrow x = 40$
Hence, the value of $x$ is $40$.

Therefore, option C is the correct answer.

Note: We must know the method of solving percentages of numbers in order to solve such problems. We should take care while doing the calculations so as to be sure of the answer. A clear idea about the concepts of transposition and simplification rules helps us to solve the problems easily. Work as many problems as possible to crack these types of problems in a limited time period.