Question

Solve and find the value of x.
$$25:x::40:160$$

Answer 1

Hint: Here, in this given question, we can use the fact that when $$::$$ symbol is given, the given two ratios are equal to each other. So, here, 25: x is equal to 40: 160. Then we can solve the thus formed equation to get the value of x.

Complete step-by-step answer:
In this given question, we are asked to solve the following equation for x,
$$25:x::40:160$$.
First of all, we must know that $$::$$ symbol is used between to ratios in order to show them as equal.
 As, $$::$$ sign is given between the two ratios, which are 25: x and 40: 160, we can know that they are equal.
So,
 $$\begin{array}{rl}& 25:x=40:160\\ & \Rightarrow {\displaystyle \frac{25}{x}}={\displaystyle \frac{40}{160}}.........(1.1)\end{array}$$
Now, solving equation 1.1 for x, we get,
$$\begin{array}{rl}& {\displaystyle \frac{25}{x}}={\displaystyle \frac{40}{160}}\\ & \Rightarrow {\displaystyle \frac{25}{x}}={\displaystyle \frac{1}{4}}\\ & \Rightarrow 25\times 4=1\times x\\ & \Rightarrow x=100.............(1.2)\end{array}$$
Hence, from equation 1.2, we get x is equal to 100.
Therefore, we have got the value of x as equal to 100.

Note: In this sort of question, we must be careful while converting ratios into fractions. The respective terms in the ratios should be respectively in the numerator and denominator. Like we can convert $$25:x=40:160$$ into $${\displaystyle \frac{25}{x}}={\displaystyle \frac{40}{160}}$$ or $${\displaystyle \frac{x}{25}}={\displaystyle \frac{160}{40}}$$ only.