Question

If $0.7$ of one number be equal to $0.075$ of another , the ratio of the two numbers is
A $3:35$
B $3:28$
C $28:3$
D $2:27$

Answer 1

Hint:
In this question let us suppose that the one number is $x$ and the other number is $y$ hence from the given question it is given that $0.7 \times x = 0.075 \times y$ now try to find out $\dfrac{x}{y}$ and that is your answer.

Complete step by step solution:
In the question it is given that the $0.7$ of one number be equal to $0.075$ of another
mean that if the one number is $x$ and the other number is $y$ than $0.7$ of $x$ is equal to the $0.075$ of $y$
This implies that $0.7 \times x = 0.075 \times y$
where $x$ and $y$ is the two numbers So we have to find out the ratio of the two number that is given in the question means $\dfrac{x}{y}$
So from the above equation $0.7 \times x = 0.075 \times y$
$\Rightarrow \dfrac{x}{y}$$ = \dfrac{{0.075}}{{0.7}}$
Multiple on RHS by $1000$ on both numerator and denominator
$\Rightarrow \dfrac{x}{y}$$ = \dfrac{{0.075 \times 1000}}{{0.7 \times 1000}}$
$\Rightarrow \dfrac{x}{y}$$ = \dfrac{{75}}{{700}}$
Both numerator and denominator are multiple of $25$ so on cancelling
$\Rightarrow \dfrac{x}{y}$$ = \dfrac{3}{{28}}$

Hence the ratio of two number is $3:28$ therefore option B is correct.

Note:
If we multiply and divide each term of ratio by the same number (non-zero), it doesn’t affect the ratio.
The ratio is used to compare the size of two things with the same unit as in the given question the first number is $\dfrac{3}{{28}}$ times of the other number.