Question

31-35 based on the following case. From a grocery shop Priyanka bought 4 kg of rice and 6 kg of flour for 1700 and Charu bought 6 kg of rice and 4 kg of flour for 1800. Consider the price of one kg of rice and that of one kg of flour be *x and y respectively.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

The price of one kg of rice be x

The price of one kg of flour be y

Further, Given that

Priyanka bought 4 kg of rice and 6 kg of flour for 1700

Cost of 4 kg of rice = 4x

Cost of 6 kg of flour = 6y

Total amount paid = 1700

$\rm \implies\:\boxed{\tt{ 4x + 6y = 1700 \: }} - - - (1)$

Further, Given that

Charu bought 6 kg of rice and 4 kg of flour for 1800.

Cost of 6 kg of rice = 6x

Cost of 4 kg of flour = 4y

Total amount paid = 1800

$\rm \implies\:\boxed{\tt{ 6x + 4y = 1800 \: }} - - - (2)$

On adding equation (1) and (2), we get

$\rm :\longmapsto\:10x + 10y = 3500$

$\red{\rm :\longmapsto\:x + y = 350 - - - (3)}$

On Subtracting equation (1) from equation (2), we get

$\rm :\longmapsto\:2x - 2y = 100$

$\red{\rm :\longmapsto\:x - y = 50 - - - (4)}$

On Adding equation (3) and (4), we get

$\rm :\longmapsto\:2x = 400$

$\bf\implies \:x = 200 - - - (5)$

On substituting (5) in equation (3), we get

$\rm :\longmapsto\:200 + y = 350$

$\bf\implies \:y = 150 - - - (6)$

Thus,

Cost of 1 kg of Rice = 200

Cost of 1 kg of flour = 150

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Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Answer 2

Given:

Priyanka bought 4 kg of rice and 6 kg of flour for 1700.

Charu bought 6 kg of rice and 4 kg of flour for 1800.

To find: The price of one kg of flour.

Solution:

Assume that,  

The price of one kg of rice is x.

The price of one kg of flour is y.

Therefore,

Cost of 4 kg of rice = 4x

Cost of 6 kg of flour = 6y

Total amount paid $= 1700$

Therefore, according to the question,

$4x+6y=1700$------(1)

And,

Cost of 6 kg of rice = 6x

Cost of 4 kg of flour = 4y

Total amount paid $= 1800$

Therefore, according to the question,

$6x+4y=1800$------(2)

Add equation (1) and (2),

$\[\begin{array}{l}10x + 10y = 3500\\ \Rightarrow x + y = 350\end{array}\]$-------(3)

Subtract equation (1) from equation (2),

$\[\begin{array}{l}2x - 2y = 100\\ \Rightarrow x - y = 50\end{array}\]$--------(4)

Add equation (3) and (4).

$\[\begin{array}{l}2x = 400\\ \Rightarrow x = 200\end{array}\]$

Substitute the value of x in equation (3),

$\[\begin{array}{l}200 + y = 350\\ \Rightarrow y = 150\end{array}\]$

Hence,

Cost of 1 kg of flour is $150$.