Question

On selling a tea set at 5% loss and a lemon set at 15% gain, a crockery seller gains 7. If he sells the tea set at 5% gain and lemon set at 10% gain, he gains 13. Find the actual price of the tea set.

Answer 1

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

The shopkeeper sells a tea set at 5 % loss and a lemon set ate 15 % gain.

So, the loss on tea set = x*5/100

And the gain on lemon set = y*15/100

Total gain = 15y/100 - 5x/100 = 70

15y - 5x = 7000

Dividing it by 5, we get

3y - x = 1400

-x + 3y = 1400...........(1)

If he sells the tea set at 5 % gain and lemon set at 10 % gain, he gains Rs 130.

Therefore,

5x/100 + 10y/100 = 130

5x + 10y = 13000

Dividing it by 5, we get

x + 2y = 2600 ..............(2)

Adding (1) and (2), we get

- x + 3y = 1400

x + 2y = 2600

______________

5y = 4000

______________

y = 4000/5

y = 800

Substituting the value of y = 800 in (2), we get

x + 2y = 2600

x + 2*800 = 2600

x + 2600 - 1600

x = 1000

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

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