Question

STD 9 th . Chapter Pairs of Equation.
The cost of 4 chairs and 5 tables is Rs.6600/- and the cost of 5 chair's and 3 table's as Rs.5000/- at the same prices . What are the prices of table and chair.​

Answer 1

Let the cost of 1 chair be  Rs. x  

    cost of the table is Rs. y  

According to the question,  

cost of 4 chairs and 3 tables is  Rs. 2100

So,  4x + 3y = 2100   ……...... (i)  

Also,

cost of 5 chairs and 2 tables is Rs.1750  

So  5x + 2y = 1750 ……….. (ii)  

from equation (i) and (ii)  

2 × (i) gives 8x + 6y = 4200  ……… (iii)  

3 × (ii) gives 15x + 6y = 5250 ……….. (iV)  

{(iii) - (iV)} ,

15x + 6y – 8x – 6y = 5250 – 4200  

7x = 1050  

x=1050/7  

So, x = 150  

putting the value of x in equation (ii), we get  

⇒  5(150) + 2y = 1750  

⇒750 + 2y = 1750  

⇒2y= 1750 – 750  

⇒2y = 1000

⇒ y =1000/2

⇒ y =500

Hence,  the cost of each chair,x = Rs. 150  

cost of each table,y = Rs. 500  

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Answer 2

Answer:

Let the cost of 1 chair be  Rs. x  

    cost of the table is Rs. y  

According to the question,  

cost of 4 chairs and 3 tables is  Rs. 2100

So,  4x + 3y = 2100   ……...... (i)  

Also,

cost of 5 chairs and 2 tables is Rs.1750  

So  5x + 2y = 1750 ……….. (ii)  

from equation (i) and (ii)  

2 × (i) gives 8x + 6y = 4200  ……… (iii)  

3 × (ii) gives 15x + 6y = 5250 ……….. (iV)  

{(iii) - (iV)} ,

15x + 6y – 8x – 6y = 5250 – 4200  

7x = 1050  

x=1050/7  

So, x = 150  

putting the value of x in equation (ii), we get  

⇒  5(150) + 2y = 1750  

⇒750 + 2y = 1750  

⇒2y= 1750 – 750  

⇒2y = 1000

⇒ y =1000/2

⇒ y =500

Hence,  the cost of each chair,x = Rs. 150  

cost of each table,y = Rs. 500