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

Answer :-

→ Actual price of the tea set = ₹ 100

→ Actual price of the lemon set = ₹ 80

Explanation :-

Let the CP of the tea set be ₹ x and CP of the lemon set be ₹ y .

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Now, according to the given conditions of the question :-

⇒ 15y/100 - 5x/100 = 7

⇒ 3y/20 - x/20 = 7

⇒ (3y - x)/20 = 7

⇒ 3y - x = 7(20)

⇒ 3y - x = 140 ----(1)

Also :-

⇒ 5x/100 + 10y/100 = 13

⇒ x/20 + y/10 = 13

⇒ (x + 2y)/20 = 13

⇒ x + 2y = 20(13)

⇒ x + 2y = 260 ----(2)

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Now, we can solve eq.1 and eq.2 to obtain our answer.

Adding eq.1 and eq.2 we get :-

⇒ 3y - x + x + 2y = 260 + 140

⇒ 5y = 400

⇒ y = 400/5

⇒ y = 80

Putting value of 'y' in eq.1 :-

⇒ 3(80) - x = 140

⇒ 240 - x = 140

⇒ x = 240 - 140

⇒ x = 100

Answer 2

Solution :-

Let the cost of tea set be x and lemon set be y

5% of x

5/100 × x

5x/100

15% of y

15/100 × y

15y/100

Now

15y/100 - 5x/100 = 7

15y - 5x/100 = 7

15y - 5x = 100 × 7

15y - 5x = 700

Now

5% of x

5/100 × x

5x/100

10% of y

10/100 × y

10y/100

5x/100 + 10y/100 = 13

5x + 10y/100 = 13

5x + 10y = 13 × 100

5x + 10y = 1300

15y - 5x + 5x + 10y = 1300 + 700

15y + 10y = 2000

25y = 2000

y = 2000/25

y = 80

By using 1

15(80) - 5x = 700

1200 - 5x = 700

-5x = 700 - 1200

-5x = -500

x = 500/5

x = 100