Question

The cost of 3 kg of apples and 2 kg of grapes on a day was found to be Rs.160. After a month the cost of 4 kg of apples and 2 kg of apples and 2 kg of grapes is Rs.300. Represent the situation as a pair of linear equations in two variables.

Answer 1

Hint: In order to solve this question assume the variables for apples and grapes. Then make equations according to the conditions provided in the question. Doing this will take you to the right answer.

Complete step-by-step answer:
Let apples be X and grapes be Y

On the first day, 3kg of apples and 2kg of grapes was 160.
So, the equation can be constructed as:
3X+2Y=160.

After one month 4kg and 2kg of apples and 2 kg of grapes was 300.
So, the equation can be constructed as:
4X+2X+2Y=300
6X+2Y=300
Taking 2 common from LHS we get the equation as:
2(3X+Y)=300
$
  {\text{3X + Y = }}\dfrac{{{\text{300}}}}{{\text{2}}} \\
  {\text{3X + Y = 150}} \\
$
Hence, the two equations are,
3X+2Y=160 ........(1)
3X+Y=150 .........(2)

On multiplying the equation (2) with 2 we get,
6X+2Y=300 …….(3)
 On subtracting equation (1) from (3) we get,
3X=140
Then we can say X=$\dfrac{{140}}{3}$
On putting the value of X in equation (2) we get the equation as:
3($\dfrac{{140}}{3}$)+Y=150
Y=150-140=10.
Hence the price of apples is $\dfrac{{140}}{3}$ per kg and price of grapes is 10 per kg.
The above equations are linear equations in two variables constructed from the conditions said in the question. Solving these two equations will give you the average price of apples and grapes of before 1 month and after one month.

Note: To solve such types of problems we have to assume the variables of the items provided and then we have to make the equations according to the conditions given in question. If the number of variables we have assumed is two then the equation formed will be a linear equation in two variables. Proceeding like this you will reach the right answer.