Math, asked by Utrasingh16, 10 hours ago

By selling a cow for Rs 144, there is a profit of the same percentage as its cost price. Find the cost price.​

Answers

Answered by tennetiraj86
31

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
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