Question

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


Quality Answer Needed!​

Answer 1

$\huge\underline\mathbb{SOLUTION:-}$

Let the cost of tea set = x.

And, the cost of lemon set = y.

If he sells tea set at 5% loss and lemon set at 15% gain.

$\implies$Loss on a tea set = $\mathsf {x\times \frac{5}{100}}$

$\implies$Gain on lemon set = $\mathsf {y\times \frac{15}{100}}$

Total gain =$\mathsf {\frac{15y}{100} - \frac{5x}{100} = 70}$

$\implies$15y - 5x = 7000

Dividing it by 5, we get:

3y - x = 1400

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

If he sells a tea set at 5% gain and the lemon set at 10% gain,

• Total gain = 130 Rs

Therefore,

$\implies \mathsf {\frac{5x}{100} + \frac{10y}{100} = 130}$

$\implies \mathsf {5x + 10y = 13000}$

Dividing it by 5, we get:

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

Add (1) and (2),we get:

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀- x + 3y = 1400

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ x + 2y = 2600

⠀⠀⠀⠀⠀⠀⠀⠀________________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀5y = 4000

⠀⠀⠀⠀⠀⠀⠀⠀________________

$\implies \mathsf {y = \frac{4000}{5}}$

$\implies \mathsf \blue {y = 800}$

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

$\implies \mathsf {x + 2y = 2600}$

$\implies \mathsf {x + 2\times800 = 2600}$

$\implies \mathsf {x + 2600 - 1600}$

$\implies \mathsf \blue {x = 1000}$

• Hence, actual price of tea set = Rs.1000 and actual price of lemon set = Rs 800.

Answer 2

$\huge{\underline{\underline{\mathfrak{Solution:-}}}}$

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.