Answer

Verified

373.2k+ views

**Hint:**We can easily solve this type of problem by finding the expression of the amount the man actually paid with the help of $x$ . Then we equate that expression to $2730$ and get a quadratic equation of variable $x$ from there. Further solving the quadratic equation by split factor method, we will get the solution of the equation i.e., the value of $x$ .

**Complete step by step solution:**

According to the given problem the price of each plant was $x$ in rupees

If the supplier has reduced the price of each plant by one rupee then the price of each plants will be $x-1$ in rupees

Earlier the man spent Rs. 2800 on buying a number of plants priced at Rs. $x$ each.

Hence, the number of plants he bought earlier was $=\dfrac{2800}{x}$

Later, he got $10$ more additional plants which makes the total number of plants he got $=\dfrac{2800}{x}+10$

Now, the total amount of money (in rupees) the man gave to the supplier according to the above expressions is

\[=\text{present price of each plant}\times \text{total number of plants}\]

$=\left( x-1 \right)\left( \dfrac{2800}{x}+10 \right)$

We equate the above expression to the given present value of net amount, $2730$as shown below

$\left( x-1 \right)\left( \dfrac{2800}{x}+10 \right)=2730$

Further, simplifying as

\[\Rightarrow \dfrac{\left( 2800+10x \right)\left( x-1 \right)}{x}=2730\]

\[\Rightarrow \left( 2800+10x \right)\left( x-1 \right)=2730x\]

\[\Rightarrow 2800x-2800+10{{x}^{2}}-10x-2730x=0\]

\[\Rightarrow 10{{x}^{2}}+60x-2800=0\]

Dividing both the terms of the above equation by $10$ we get

\[\Rightarrow {{x}^{2}}+6x-280=0\]

Using the split factor method as shown below

\[\Rightarrow {{x}^{2}}+20x-14x-280=0\]

\[\Rightarrow x\left( x+20 \right)-14\left( x+20 \right)=0\]

\[\Rightarrow \left( x+20 \right)\left( x-14 \right)=0\]

Now,

$x+20=0$ and \[x-14=0\]

Simplifying we get $x=-20,14$

As, $x$ is the price of each plant it can’t be negative. So, we only consider the solution $x=14$

**Therefore, we conclude that the value of $x$ is $14$.**

**Note:**We must be careful while making the expressions of the amount the man actually paid with the help of $x$ as, an incorrect expression of the same can cause unavoidable mistakes. Also, it is not necessary to solve the quadratic equation by split factor method. It can also be solved using Sridhar Acharya’s formula or by completing a square.

Recently Updated Pages

If O is the origin and OP and OQ are the tangents from class 10 maths CBSE

Let PQ be the focal chord of the parabola y24ax The class 10 maths CBSE

Which of the following picture is not a 3D figure a class 10 maths CBSE

What are the three theories on how Earth was forme class 10 physics CBSE

How many faces edges and vertices are in an octagonal class 10 maths CBSE

How do you evaluate cot left dfrac4pi 3 right class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail

Name 10 Living and Non living things class 9 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths