Question

On selling a tea-set at 5% loss and a lemon set at 15% gain, a crockery seller gains Rs. 7. If he sells the tea set at 5% gain and the lemon set at 10% gain, he gains Rs. 13. Find the actual price of the tea set and the lemon set\
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Answer 1

Given:-

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

To Find:-

• the actual price of the tea set and the lemon set.

Solution:-

• Let The Cost Of Tea set= Rs. x

• Let the cost of Lemon set= Rs. y

According to the Question:-

1)

there's a Loss on selling Tea set

So, Loss on selling Tea set= $\frac{ Rs. 5 \times x}{100} = \frac{x}{20}$

And There's a Gain in Selling Lemon set

So, Gain In Selling Lemon set= $\frac{ Rs. 15 \times y}{100} = \frac{3y}{20}$

It Is Given that,

On selling a tea-set at 5% loss and a lemon set at 15% gain, a crockery seller gains Rs. 7.

That Means:

Gain on Selling Lemon Set Should Be Subtracted from Loss of Selling Tea set

As Seller is Gaining By Rs.7

So,

$\frac{3y}{20} - \frac{x}{20} = 7$

$= > \frac{3y - x}{20} = 7$

$= > 3y - x = 140..(1)$

2)

There's a Gain on Selling Tea set

So, Gain on Selling tea set= $\frac{Rs.5 \times x}{100} = \frac{Rs.x}{20}$

And There's a Gain in Selling Lemon set

So, Gain In Selling Lemon set= $\frac{Rs.10 \times y}{100} = \frac{Rs.y}{10}$

Also,

It is given That,

If he sells the tea set at 5% gain and the lemon set at 10% gain, he gains Rs. 13.

Which means:

Gain on Selling Tea set should be added in Gain on Selling Lemon set to Give Gain of Rs 13.

So,

$\frac{x}{20} + \frac{y}{10} = 13$

$= > \frac{x}{20} + \frac{2y}{20} = 13$

$= > \frac{x + 2y}{20} = 13$

$= > x + 2y = 13 \times 20$

$= > x + 2y = 260..(2)$

Now For Finding the Values, We will solve Equation (1) and (2).

$3y - x = 140$

and

$x + 2y = 260$

Adding Both the equations

$3y - x + x + 2y = 140 + 260$

$= > 5y = 400$

$= > y = 80$

Now, Putting the value of y in Equation (1).

$3 \times 80- x = 140$

$= > 240 - 140 = x$

$= > x = 100$

Answer 2

Answer:

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