A man sold a chair and a table together for Rs.1520 thereby making a profit of 25% on the chair and 10% on the table. By selling them together for Rs.1535 he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each

A man sold a chair and a table together for Rs.1520 thereby making a profit of 25% on the chair and 10% on the table. By selling them together for Rs.1535 he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each

1. A
2. B
3. C
4. D

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Solution:

Concept: In order to solve the given question, first we will assume 2 variables for the cost price of each. Finding relation between two variables using condition 1. Similarly from the second condition you have 2 equations of 2 variables. So, apply a substitution method to solve and get the required answer.
Here,

$=\frac{100x+25x}{100}=\frac{5}{4}x.$

$\frac{100y+10y}{100}=\frac{11}{10}y.$
$\frac{5}{4}x+\frac{11}{10}y=1520$
$25x+22y=30400\dots \dots ..\left(1\right)$
Now,

$\frac{11}{10}x+\frac{5}{4}y=1535$
$22x+25y=30700\dots \dots \dots \left(2\right)$
Now, substrate equation (2) from(1) we will get,

$x-y=-100\dots \dots \dots .\left(3\right)$
Now Add equation (2) and (1) , we will get,
$47x+47y=61100$
$x+y=1300\dots \dots \dots \dots \left(4\right)$
Then solve equation ( 3) and (4) ,

$x+y=1300$
$=>2x=1200$
$x=600$
Now putting The value of x in equation (3)

$-y=-700$
$y=700$
Therefore,

Hence, the correct option is 2.

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