A man sold a chair and table for ₹12000 gaining 10% on chair and 15% on table. Had he sold the for 11625, the profit would've interchanged. Find the C.P.
I want to see how can we find it by adding and subtracting the coefficients. no copy paste
Answers
Step-by-step explanation:
Given :-
A man sold a chair and table for ₹12000 gaining 10% on chair and 15% on table. Had he sold the for 11625, the profit would've interchanged.
To find :-
Find the C.P. of each item ?
Solution :-
Let the Cost price of the chair be Rs. X
Let the Cost Price of the table be Rs. Y
Profit on the chair = 10% of the CP
=> Profit = 10% of X
=> Profit = (10/100)×X
=> Profit = 10X/100
=> Profit = Rs. X/10
We know that
Selling Price = Cost Price + Profit
=> SP = X+(X/10)
=>SP = (10X+X)/10
=> SP of the chair = Rs. 11X/10 ----------(1)
Profit on the table = 15% of the CP
=> Profit = 15% of Y
=> Profit = (15/100)×Y
=> Profit = 15Y/100
=> Profit = Rs. 3Y/20
We know that
Selling Price = Cost Price + Profit
=> SP = Y+(3Y/20)
=>SP = (20Y+3Y)/20
=> SP of the table = Rs. 23Y/20 ----------(2)
According to the given problem
A man sold a chair and table for ₹12000 gaining 10% on chair and 15% on table.
=> (11X/10)+(23Y/20) = 12000
LCM of 10 and 20 = 20
=> (22X+23Y)/20 = 12000
=> 22X+23Y = 12000×20
=> 22X+23Y = 240000 ----------(3)
If he sold it for Rs. 11625 the profit Percentages are interchanged
=> Profit on chair = 15% of CP
=> Profit = 15% of X
=> Profit = (15/100)×X
=> Profit = 15X/100
=> Profit = Rs. 3X/20
We know that
Selling Price = Cost Price + Profit
=> SP = X+(3X/20)
=>SP = (20X+3X)/20
=> SP of the table = Rs. 23X/20 ----------(4)
Profit on the table = 10% of the CP
=> Profit = 10% of Y
=> Profit = (10/100)×Y
=> Profit = 10Y/100
=> Profit = Rs. Y/10
We know that
Selling Price = Cost Price + Profit
=> SP = Y+(Y/10)
=>SP = (10Y+Y)/10
=> SP of the chair = Rs. 11Y/10 ----------(5)
According to the given problem
=> ( 23X/20) + (11Y/10) = 11625
LCM of 10 and 20 = 20
=> (23X+22Y)/20 = 11625
=> 23X+22Y = 11625×20
=> 23X+22Y = 232500 ----------(6)
On adding (3) and (6)
22X+23Y = 240000
23X+22Y = 232500
(+)
_______________
45X+45Y = 472500
_______________
=> 45X+45Y = 472500
=> 45(X+Y) = 472500
=> X+Y = 472500/45
=> X+Y = 10500-----------(7)
On subtracting (6) from (3)
22X+23Y = 240000
23X+22Y = 232500
(-)
_______________
-X+Y = 7500
_______________
=>- X+Y = 7500
=> X-Y = -7500 ----------(8)
On adding (7)&(8)
X+Y = 10500
X-Y = 7500
(+)
___________
2X+0 = 3000
___________
=> 2X = 3000
=> X = 3000/2
=> X = 1500
On Substituting the value of X in (7) then
=> 1500+Y = 10500
=>Y = 10500-1500
=> Y = 9000
Therefore, X = Rs. 1500 and Y = Rs. 9000
Answer:-
The Cost Price of the chair = Rs. 1500
The Cost Price of the table = Rs. 9000
Used formulae:-
- Selling Price > Cost Price = Profit
- Selling Price = Cost Price + Profit