A person buy 5 table and 9 chairs for rs 15400.he sells table at 10% profit and chairs at 20%.profit.if his total profit on selling all tables and chairs is 2080rs.find cost price 9f 3 chairs
Answers
Answer:
formula of cp 100/(100 - loss%)*sp
Step-by-step explanation:
put the formula
The cost price of 3 chairs is Rs. 1,800.
• Given,
Number of tables bought = 5
Number of chairs bought = 9
• Let the cost price of each table be x.
∴ The cost price of 5 tables = 5x
Let the cost price of each chair be y.
∴ The cost price of 9 chairs = 9y
• According to the question,
Cost of 5 tables + Cost of 9 chairs = Rs. 15400
=> 5x + 9y = Rs. 15,400 -(i)
• Also given,
Profit earned on selling 5 tables = 10 %
Profit earned on selling 9 chairs = 20 %
Total profit earned = Rs. 2,080
• Now, profit is always earned on the cost price of an article.
Therefore, if the C.P. of 5 tables is 5x, then the profit earned on their C.P. = 10 % of 5x
= (10 / 100) × 5x
= (10 × 5x) / 100
= 50x / 100
• Similarly, the profit earned on the C.P. of 9 chairs = 20 % of 9y
= (20 / 100) × 9y
= (20 × 9y) / 100
= 180y / 100
• According to the question,
(50x / 100) + (180y / 100) = Rs. 2,080
=> ( 50x + 180y) / 100 = Rs. 2,080
=> 50x + 180y = Rs. 2,080 × 100
=> 10 ( 5x + 18y ) = Rs. 2,080 × 100
=> 5x + 18y = ( Rs. 2,080 × 100 ) / 10
=> 5x + 18y = Rs. 20,800 -(ii)
• Now, the equations (i) and (ii) can be solved simultaneously by subtracting (i) from (ii).
• Subtracting eq. (i) from eq. (ii), we get,
( 5x + 18y ) - ( 5x + 9y ) = Rs. 20,800 - Rs. 15,400
=> 5x + 18y - 5x - 9y = Rs. 5,400
=> 5x - 5x + 18y - 9y = Rs. 5,400
=> 0 + 9y = Rs. 5,400
=> 9y = Rs. 5,400
=> y = Rs. 5,400 / 9
=> y = Rs. 600
• As stated earlier, y represents the cost price of each chair.
∴ The cost price of each chair = Rs. 600
=> The cost price of 3 chairs = 3 × Rs. 600 = Rs. 1,800 (Answer)