Form the equations of the question above.
Class 10th rd sharma pair of linear equations in two variables.
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7. Jamila sold a table and a chair for ₹ 1050, thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair, she would have got ₹ 1065. Find the cost price of each.
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Solution:
Let the cost price of one table and one chair be ₹ x and ₹ y, respectively.
So,
The selling price of the table, when it’s sold at a profit of 10% = ₹ x + 10x/100 = ₹ 110x / 100
The selling price of the chair, when it’s sold at a profit of 25% = ₹ y + 25y/100 = ₹ 125y / 100
Hence, according to the question
110x / 100 + 125y / 100 = 1050 … (i)
Similarly,
The selling price of the table, when it’s sold at a profit of 25% = ₹ (x + 25x/100) = ₹ 125x/ 100
The selling price of the chair, when it’s sold at a profit of 10% = ₹ (y + 10y/100) = ₹ 110y / 100
Hence, again from the question,
125x / 100 + 110y / 100 = 1065 … (ii)
Re-written (i) and (ii) with their simplest coefficients,
11x/10 + 5y/4 = 1050…….. (iii)
5x/4 + 11y/10 = 1065…….. (iv)
Adding (iii) and (iv), we get
(11/ 10 + 5/ 4)x + (5/ 4 + 11/ 10)y = 2115
47/ 20x + 47/ 20y = 2115
x + y = 2115(20/ 47) = 900
⇒ x = 900 – y ……. (v)
Using (v) in (iii),
11(900 – y)/10 + 5y/4 = 1050
2(9900 -11y) +25y = 1050 x 20 [After taking LCM]
19800 – 22y + 25y = 21000
3y = 1200
⇒ y = 400
Putting y = 400 in (v), we get
x = 900 – 400 = 500
Therefore, the cost price of the table is ₹ 500 and that of the chair is ₹ 400.