Question

A man sold a table and chair for Rs. 850 at a loss of 10% on the table and a gain of 10% on the chair. By selling them together for Rs. 950 he would have made a gain of 10% on the table and loss of 10% on the chair. Find the cost price of each.

Answer 1

Answer :

Let us consider that cost price of the table is Rs x and that of the chair is Rs y.

In the 1st case,

Selling price of the table
= Rs (100 - 10)x/100
= Rs 90x/100
= Rs 9x/10

and selling price of the chair
= Rs (100 + 10)y/100
= Rs 110y/100
= Rs 11y/10

By the given condition,
9x/10 + 11y/10 = 850

⇒ 9x + 11y = 8500 ...(i)

In the 2nd case,

Selling price of the table
= Rs (100 + 10)x/100
= Rs 110x/100
= Rs 11x/10

and selling price of the chair
= Rs (100 - 10)y/100
= Rs 90y/100
= Rs 9y/10

By the given condition,
11x/10 + 9y/10 = 950

⇒ 11x + 9y = 9500 ...(ii)

We have found two equations :

9x + 11y = 8500 ...(i)
11x + 9y = 9500 ...(ii)

Now, multiplying (i) by 11 and (ii) by 9, we get

99x + 121y = 93500
99x + 81y = 85500

On subtraction, we get

121y - 81y = 93500 - 85500

⇒ 40y = 8000

⇒ y = 8000/40

⇒ y = 200

From (i), we get

9x + (11 × 200) = 8500

⇒ 9x + 2200 = 8500

⇒ 9x = 8500 - 2200

⇒ 9x = 6300

⇒ x = 6300/9

⇒ x = 700

∴ the cost price of the table is Rs 700 and the cost price of the chair is Rs 200

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Answer 2

..............here is your answer