Question

If 12% of x is equal to 6% of y, then 18% of x will be equal to how much percent of y?
A.7%
B.9%
C.8%
D.11%

Answer 1

Hint: First of all, 12% of x means $\dfrac{{12}}{{100}} \times x$ and 6% of y means $\dfrac{6}{{100}} \times y$. So, form an equation firstly for this. Now, we need to find what percent of y is equal to 18% of x. So, we need to get $\dfrac{{18}}{{100}} \times x$ in the LHS of the equation. For that, multiply $\dfrac{{12}}{{100}} \times x$ with some number to make it $\dfrac{{18}}{{100}} \times x$.

Complete step-by-step answer:
In this question, we are given that there are two numbers x and y and 12% of x is equal to 6% of y. Based on this, we need to find what percent of y will be 18% of x.
So, first of all let us form an equation for 12% x equal to 6% y. Therefore, we get
$ \Rightarrow $12% of x$ = $6% of y
$ \Rightarrow \dfrac{{12}}{{100}} \times x = \dfrac{6}{{100}} \times y$- - - - - - - - - (1)
So, to find 18% of x, we need to get $\dfrac{{18}}{{100}} \times x$ in the LHS of the equation.
Now, to get $\dfrac{{18}}{{100}} \times x$ in LHS, we need to multiply $\dfrac{{12}}{{100}}$ with some number.
Let $\dfrac{{12}}{{100}} \times z = \dfrac{{18}}{{100}}$. Therefore,
$
   \Rightarrow 12 \times z = 18 \\
   \Rightarrow z = \dfrac{{18}}{{12}} = \dfrac{3}{2} \;
 $
Therefore, we need to multiply $\dfrac{{12}}{{100}}$ with $\dfrac{3}{2}$ to get $\dfrac{{18}}{{100}}$ in LHS.
Therefore, multiplying equation (1) with $\dfrac{3}{2}$, we get
$
   \Rightarrow \dfrac{{12}}{{100}} \times \dfrac{3}{2} \times x = \dfrac{6}{{100}} \times \dfrac{3}{2} \times y \\
   \Rightarrow \dfrac{{18}}{{100}} \times x = \dfrac{9}{{100}} \times y \;
 $
$ \Rightarrow $18% of x$ = $9% of y
Therefore, 18% of x will be equal to 9% of y.
Hence, option B is our correct answer.
So, the correct answer is “Option B”.

Note: Here, we can also solve this question using the method of cross multiplication.
12% of x $ = $ 6% of y
18% of x $ = $ ? % of y
$ \Rightarrow $18% of x $ = \dfrac{{\dfrac{{18}}{{100}} \times x \times \dfrac{6}{{100}} \times y}}{{\dfrac{{12}}{{100}} \times x}}$
$
   = \dfrac{{18 \times 6 \times x \times y \times 100}}{{12 \times 100 \times 100 \times x}} \\
   = \dfrac{9}{{100}} \times y \\
 $
$ = $ 9% of y