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A man sold a table and a chair together for ₹850 at a loss of $10 %$ on the table and a gain of $10 %$ on the chair. By selling them together for ₹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.

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The cost of a chair is ₹200 and the cost of a table is ₹600

The cost of a chair is ₹200 and the cost of a table is ₹700

The cost of a chair is ₹300 and the cost of a table is ₹400

The cost of a chair is ₹100 and the cost of a table is ₹700

answer is A.

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Detailed Solution

It is given that a man sold a table and a chair together for ₹ 850 at a loss of

10 %

on the table and a gain of

10 %

on the chair.
It is also given that by selling them together for ₹ 950, he would have made a gain of

10 %

on the table and loss of

10 %

on the chair.
Let the cost of the chair be

x

and the cost of the table be

y

.
There is a loss of 10% on table and gain of 10% on chair.

L o s s o f 10 % o n t a b l e = 10100 × y L o s s o f 10 % o n t a b l e = y 10 g a i n o f 10 % o n c h a i r = 10100 × x g a i n o f 10 % o n c h a i r = x 10

As he sold a table and a chair together for ₹ 850 at a loss of 10% on the table and a gain of 10% on the chair,

\Rightarrow (x + \frac{x}{10}) + (y - \frac{y}{10}) = 850

\Rightarrow \frac{11 x}{10} - \frac{9 y}{10} = 850

\Rightarrow 11 x - 9 y = 8500

…….(1)
By selling them together for ₹ 950, he would have made a gain on 10% on the table and loss of 10% on the chair.

\Rightarrow (x - \frac{x}{10}) + (y + \frac{y}{10}) = 950

\Rightarrow \frac{9 x}{10} + \frac{11 y}{10} = 950

\Rightarrow 9 x + 11 y = 9500

…….(2)
Solving equations (1) and (2) to determine the value of

x

and

y

⇒ x − 85500 + 93500 = − y − 104500 + 76500 = 1 121 − 81 ⇒ x 8000 = − y − 28000 = 140 ⇒ x 8000 = y 28000 = 140

We get the values,

⇒ x 8000 = 140 ⇒ x = 200

And,

⇒ y 28000 = 140 ⇒ y = 700

The cost of a chair is ₹200 and the cost of a table is ₹700.
Hence, the correct option is 1.

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