Question

Paint is red: blue in a ratio 3: 4. If 6 liters of blue is used, how much red?

Answer 1

Hint: Here in this we have to find how much red paint is used. The question is belonging to ratio and proportion. So we have to use the ratio and proportion concept to solve it. Here we use the basic simple mathematical operations to solve further. Hence we have obtained the required solution for the question.

Complete step by step solution:
A ratio is a comparison of two quantities. The ratio of a to b can also be expressed \[a:b\] or \[\dfrac{a}{b}\] . A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.
Here we have two paints, one is red and the other one is blue. The paints are in the ratio 3:4.
The given data is written in the ratio and proportion as
 \[3:4::x:6\]
the above equation is written as
 \[ \Rightarrow \dfrac{3}{4} = \dfrac{x}{6}\]
Take 6 to LHS, the equation is written as
 \[ \Rightarrow \dfrac{{6 \times 3}}{4} = x\]
On simplifying the above equation is written as
 \[ \Rightarrow x = \dfrac{{18}}{4}\]
On dividing by 4 we get
 \[ \Rightarrow x = 4.5\]
Therefore the 4.5 litres of red paint is used.
Hence we have determined the solution for the given question.
So, the correct answer is “4.5 litres”.

Note: The ratio is written in the form of fraction. While simplifying we use the simple arithmetic or mathematical operations. The arithmetic operations are addition, subtraction, multiplication and division. The unknown term can be written in the form of variable. let it x or y or any variable.