Question

a man sold a chair and table together for rupees 760, thereby making a profit of 25% on chair and 10% on table post of by selling them together for rupees 767. 50, he would have made a profit of 10% on the chair and 25% on the table. find the cost price of each​

Answer 1

$\huge\mathfrak\green{Answer:-}$

We can solve this by using linear equations.

Let the price of the table be y and that of the chair be x:

Equation 1:

Price of chair at 25% profit will be 1.25x (that is 125% of marked price x) and profit is 0.25x

price of table at 10% profit is 1.1y (that is 110% of y)

Therefore   1.1y + 1.25x= Rs.760

Equation 2:

price of chair at 10% profit = 1.1x

price of table at 25% profit= 1.25y

Therefore 1.1x + 1.25y = 767.5

Solve for x and y:

1.25x+1.1y= 760

1.1y= 760-1.25x

y= (760-1.25x)/1.1

1.1x+1.25y= 767.5

substitute y in the second equation

1.1x + 1.25((760-1.25x)/1.1)=767.5

1.21x+950-1.5625x= 844.25

-0.3525x= -105.75

 x=  300

Now, substitute x in any of the above equations to find y:

1.1y=760- 1.25x

1.1y= 760- 375

1.1y= 385

y=  350

Therefore the cost price of the chair=  Rs. 300 and that of the table = Rs.350.

Answer 2

Answer:

$\implies$ The cost price of the chair = Rs.300 and that of the table = Rs.350.

$\large\underline\mathrm{Given:-}$

• A man sold a chair and table together for rupees 760, thereby making a profit of 25% on chair and 10% on table post of by selling them together for rupees 767. 50
• A profit of 10% on the chair and 25% on the table.

$\large\underline\mathrm{To \: find}$

• We can solve by using linear equations.

$\large\underline\mathrm{Solution}$

• let let the price of the table by y And that of the chair be x;

Equation (1).

So, price of chair at 25% profit will be 1.25x (that is 125% of maked price x) and profit is 0.25x.

price of table at 10% profit is 1.1y (that is 110% of y)

Therefore 1.1y + 1.25x = Rs.760

Equation (2).

$\implies$ price of the chair at 10% profit = 1.1x

$\implies$ price of table at 25% profile = 1.25y

Therefore

$\implies$ 1.1x + 1.25y = 767.5

$\implies$ solve the x and y

$\implies$ 1.25x + 1.1y = 760

$\implies$ 1.1y = 760 - 1.25x

$\implies$ y = (760 - 1.25x)/1.1

$\implies$ 11x + 1.25y = 767.5

Substitute y in the second equation.

$\implies$1.1x + 1.25((760 - 1.25x)/11) = 767.5

$\implies$ 1.21x + 950 - 1.5625x = 844.25

$\implies$ -0.3525x = -105.75

$\implies$ x = 300

Now, substitute x in any of the equation to find y;

$\implies$ 1.1y = 760 - 1.25x

$\implies$ 1.1y = 760 - 375

$\implies$ 1.1y = 385

$\implies$ y = 350.

Hence,

The cost price of the chair = Rs.300 and that of the table = Rs.350.