Question

On selling a tea set at 10% loss and a lemon set at 20% gain, a shopkeeper gains Rs. 60. If he sells tea

set at 5% gain and lemon set at 5 % loss be gains Rs. 10. Find the cost price of tea set and the lemon

set.

Answer 1

Solution :-

Let the cost price of the tea set be Rs. 'x' and the cost price of the lemon set be Rs. 'y'.

By selling the tea set at 10 % loss and selling the lemon set at 20 % gain, the shopkeeper gains Rs. 60. Loss is denoted as negative sign.

⇒ (- x*10)/100 + (y*20)/100 = 60

⇒ - x/10 + 2y/10 = 60/1

Taking L.C.M. of the denominators and solving it.

⇒ - x + 2y = 600 ...........(1)

Now, second condition.

By selling the tea set at 5 % gain and selling lemon set at 5 % loss, the shopkeeper gains Rs. 10

⇒ (x*5)/100 - (y*5)/100 = 10

⇒ x/20 - y/20 = 10/1

Taking L.C.M. of the denominators and solving it, we get.

⇒ x - y = 200 ...........(2)

Adding (1) and (2), we get

  - x + 2y = 600
    x -  y   = 200
________________

         y   =  800
________________

Putting the value of y = 800 in (1), we get.

⇒ - x + 2y = 600

⇒ - x + 2*800 = 600

⇒ - x + 1600 = 600

⇒ - x = 600 - 1600

⇒ - x = -1000

⇒ x = 1000

Hence, the cost price of the tea set is Rs. 1000 and the cost price of the lemon set is Rs. 800.

Answer.
 

Answer 2

Let the cost price of tea set be Rs x

So the cost price of lemon set be Rs y

Case I:

(-x*10/100) + (y*20/100) =60

-x/10 + y/10 = 60

-x + 2y / 10 = 60

-x + 2y = 600 ______(i)

Case II:

(x*5/100) - (y*5/100) = 10

x/20 - y/20 = 10

x - y = 200_________(ii)

Eq (i) + Eq (ii) gives ,

-x + 2y = 600

x - y = 200

___________

y = 800

x - y =200

x - 800 = 200

x = 200 + 800

x = 1000

So , the cost price of tea set is Rs 1000 and the cost price of lemon set Rs 800 .