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# If the rate of ghee increases by ${\text{Rs}}.30\;{\text{per}}\;{\text{kg}}$, one would receive $1\;{\text{kg}}$ ghee less for ${\text{Rs}}.900$. Find the original rate of ghee per kg.

Last updated date: 13th Jun 2024
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Hint:Choose variables to represent unknown, write down the equation for the given problem in terms of assumed unknown and solve the equation to find the value of the original rate of ghee per kilogram.

Complete step by step solution:
A word problem is a mathematical practice where significant information on the problem is presented in ordinary form rather than in mathematical expression. A word problem is a maths question written as one sentence or more that requires children to apply their maths knowledge to a real-life scenario.
The easiest way to solve the word problem is to represent unknown numbers with variables, translate the rest of the word problem into a mathematical expression and finally solve the problem. Word problem is a technique of thinking how to determine the problem and solve it.
Let $x$ be the original rate of ghee.
Then,
According to question,
The new rate of ghee is ${\text{Rs}}.\left( {x + 30} \right)\;{\text{per}}\;{\text{kg}}$……..(1)
The original rate of ghee for ${\text{Rs}}.900$is $\dfrac{{900}}{x}\;{\text{kg}}$………(2)
The new quantity of ghee at new price is $\dfrac{{900}}{{x + 30}}\;{\text{kg}}$………(3)
Now, one would receive $1\;{\text{kg}}$of ghee for ${\text{Rs}}.900$.
Thus, the new quantity of ghee is equal to the original quantity of ghee minus one.
Therefore,$\dfrac{{900}}{{x + 30}} = \dfrac{{900}}{x} - 1$……..(4).
Solve the above equation as,
${x^2} + 30x - 2700 = 0 \\ \left( {x + 180} \right)\left( {x - 150} \right) = 0 \\ x + 180 = 0 \\ x - 150 = 0 \\$
Substitute both the phrases equals to zero,
$x = - 180 \\ x = 150 \\$
It is known that the rate cannot be negative. Therefore, the original rate of ghee is $x = 150$.

Hence, the option B is correct.

Note:On solving the word problems always be careful where you need to take the English words and solve them into mathematics. These types of questions are always based on representing the unknown numbers with variables on the given information.