Question

On selling a tea-set at 5% loss and a lemon-set at 15% gain , a shopkeeper gain's 84 . However , if he sells the tea-set at 5% gain and the lemon - set at 10% gain , he gains 104 . Find the price of the tea-set and that of the lemon-set paid by the shopkeeper.

Answer 1

Let the CP of the tea set and the lemon set be Rs X and Rs Y respectively.



Then, Loss on tea set = Rs ( X × 5 / 100 ) = Rs X/20.



And,

Gain on lemon set = Rs ( Y × 15 / 100 ) = Rs 3Y/20.



Therefore,

Net Gain = Rs ( 3Y/20 - X/20 )



84 = ( 3Y/20 - X/20 )




3Y - X = 1680 -------------(1)


Again , gain on tea set = Rs ( X × 5/100 ) = Rs X/20.


And,

Gain on lemon set = Rs ( Y × 10 /100 ) = Y/10.


Total gain = Rs ( X/20 + Y /10 )



104 = X /20 + Y/10




X + 2Y = 2080 --------(2)


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


5Y = 3760


Y = 752




Putting y = 752 in equation (2) , we get:



X + ( 2 × 752 ) = 2080



X = ( 2080 - 1504 )


X = 576



Therefore,


X = 576 and Y = 752


Hence,

CP of the tea set = Rs 576


And,

CP of the lemon set = Rs 752.