Question

1.
A man purchased a chair and a table for Rs. 550. He sold
the chair at a loss of 5% and the table at a profit of 10%, and
thereby made an overall profit of 4%. What was the cost price of
the chair? Ans. 210 tot
IWBCS Exam., 1989)​

Answer 1

Given:

A man purchased a chair and a table for Rs. 550.

He sold  the chair at a loss of 5% and the table at a profit of 10% and

thereby made an overall profit of 4%

To find:

What was the cost price of  the chair?

Formula Used:

$\boxed{\bold{S.P. = \frac{100 + G\%}{100} \times C.P. }}\\\\\boxed{\bold{S.P. = \frac{100 - L\%}{100} \times C.P. }}$

Solution:

Let's assume the cost of the chair be "x".

Then, the cost of the table will be "(550 - x)".

Since the man sold the chair at a loss of 5%

∴ S.P. of the chair = $\frac{100 - 5}{100}\times x = \frac{95}{100}x$

Since the man sold the table at a profit of 10%

∴ S.P. of the table = $\frac{100 +10}{100}\times (550 -x) = \frac{110}{100}(550 - x)$

Also, since the total C.P. of a chair and a table is Rs. 550 and the overall profit is 4 %

∴ Total S.P. = $\frac{100 + 4}{100}\times 550 = \frac{104}{100}\times 550 = \frac{57200}{100} = 572$

Now, according to the question, we get

[S.P. of a chair] + [S.P. of a table] = [Total S.P. of a chair and table]

$\implies \frac{95}{100}x + \frac{110}{100}(550 - x) = 572$

$\implies 0.95x + 1.1(550 - x) = 572$

$\implies 0.95x + 605 - 1.1x = 572$

$\implies 1.1x - 0.95x = 605 - 572$

$\implies 0.15x =33$

$\implies x = \frac{33}{0.15}$

$\implies \bold{x = 220}$

Thus, the cost price of the chair was → Rs. 220.

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