By selling a cow for Rs 144, there is a profit of the same percentage as its cost price. Find the cost price.
Answers
Step-by-step explanation:
Given :-
By selling a cow for Rs 144, there is a profit of the same percentage as its cost price.
To find :-
Find the cost price?
Solution :-
Given that
The selling price of a cow = Rs. 144
Let the profit on it be Rs. X%
According to the given problem
The Cost Price = Profit = Rs. X
We know that
Cost price = (100×SP)/(100+g)
We have,
SP = Rs. 144
g = X
On Substituting these values in the above formula then
=> X = (100×144)/(100+X)
=> X = 14400/(100+X)
=> (100+X)(X) = 14400
=> 100X+X² = 14400
=> X²+100X = 14400
=> X²+100X-14400 = 0
=> X²+180X-80X -14400 = 0
=> X(X+180)-80(X+180) = 0
=> (X+180)(X-80) = 0
=> X+180 = 0 (or) X -80 = 0
=> X = -180 (or) X = 80
X can't be negative since it is the price of the cow
Therefore, X = Rs. 80
Alternative Method:-
The selling price of a cow = Rs. 144
Let the profit on it be Rs. X%
According to the given problem
The Cost Price = Profit = Rs. X
We know that
Profit = X% of X
=> (X/100)×X
=> X²/100
We know that
Selling Price = Cost Price+Profit
=> 144 = X+(X²/100)
=> 144 = (100X+X²)/100
=> 144×100 = 100X+X²
=> 14400 = 100X+X²
=> X²+100X-14400 = 0
=> X²+100X-14400 = 0
=> X²+180X-80X -14400 = 0
=> X(X+180)-80(X+180) = 0
=> (X+180)(X-80) = 0
=> X+180 = 0 (or) X -80 = 0
=> X = -180 (or) X = 80
X can't be negative since it is the price of the cow
Therefore, X = Rs. 80
Answer:-
The Cost Price of the cow = Rs. 80
Check:-
Cost price of the Cow = Rs. 80
Profit on it = 80%
(Since Profit% is as the CP)
We know that
Selling Price = (100+g)CP/100
=> SP = (100+80)×80/100
=> SP = 180×80/100
=> SP = 14400/100
=> SP = Rs. 144
Selling Price of the cow = Rs. 144
Verified the given relations in the given problem.
Used formulae:-
→ Cost price = (100×SP)/(100+g)
→ Selling Price = (100+g)CP/100
→ Selling Price = Cost Price+Profit
- SP = Selling Price
- CP = Cost Price
- g = gain or profit