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Q.

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

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a

C . P . of chair = Rs . 800, C . P . of table = Rs . 500

b

C . P . of chair = Rs . 600, C . P . of table = Rs . 700

c

C . P . of chair = Rs . 800, C . P . of table = Rs . 700

d

C . P . of chair = Rs . 600, C . P . of table = Rs . 500

answer is B.

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Detailed 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,

cost of 1 chair = x and cost of one table = y

profit on chair = 25 % then SP of chair = x + \frac{25}{100} x

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

profit on table = 10 % then SP of table = y + \frac{10}{100} y

\frac{100 y + 10 y}{100} = \frac{11}{10} y .

\frac{5}{4} x + \frac{11}{10} y = 1520

25 x + 22 y = 30400 \dots \dots . . (1)

Now,

profit on chair = 10 % then SP = x + \frac{10}{100} x = \frac{100 x + 10 x}{100} = \frac{11}{10} x

profit on table = 25 % then SP of table = y + \frac{25}{100} y = \frac{100 y + 25 y}{100} = \frac{5}{4} y

\frac{11}{10} x + \frac{5}{4} y = 1535

22 x + 25 y = 30700 \dots \dots \dots (2)

Now, substrate equation (2) from(1) we will get,

3 x - 3 y = - 300

x - y = - 100 \dots \dots \dots . (3)

Now Add equation (2) and (1) , we will get,

47 x + 47 y = 61100

x + y = 1300 \dots \dots \dots \dots (4)

Then solve equation ( 3) and (4) ,

x - y = - 100

x + y = 1300

= > 2 x = 1200

x = 600

Now putting The value of x in equation (3)

600 - y = - 100

- y = - 700

y = 700

Therefore,

CP of chair = Rs . 600 and CP of table = Rs . 700

Hence, the correct option is 2.

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