Question

P sold a car to Q at a profit of 15% and Q sold the car to S at a profit of 10%. If S bought the car in
Rs.25,30,000 then what is the cost price of car for Q?
​

Answer 1

Step-by-step explanation:

Given :-

P sold a car to Q at a profit of 15% and Q sold the car to S at a profit of 10%. S bought the car in Rs.25,30,000 .

To find :-

What is the cost price of car for Q?

Solution :-

Given that

Let the cost price of the car for P be

Rs. X

Profit on a car is sold by P to Q = 15%

We have , CP = Rs. X , g% = 15%

We know that

Selling Price = [(100+g)/100]×CP

=> SP = [(100+15)/100]×X

=> SP = (115/100)×X

=> SP = (23/20)X

=> SP = Rs. 23X/20

Selling Price of the car = Rs. 23X/20

P sold the car to Q for Rs. 23X/20

So, Cost Price of the car for Q

= Rs. 23X/20

Q is sold the car to S at a profit of 10%

We know that

Selling Price = [(100+g)/100]×CP

=> SP = [(100+10)/100](23X/20)

=> SP = (110/100)×(23X/20)

=> SP = (11/10)(23X/20)

=> SP = (11×23X)/(10×20)

=> SP = 253X/200

Selling Price of the car = Rs. 253X/200

Q sold the car to S for Rs. 253X/200

Cost price of the car for S = Rs.253X/200

According to the given problem

S bought the car for Rs.25,30,000

=> 253X/200 = 2530000

=> 253X = 2530000×200

=> X = (2530000×200)/253

=> X = 10000×200

=> X = 20,00,000

Original cost price of the car of P

= Rs. 20,00,000

Now,

Cost Price of the car for Q = Rs. 23X/20

=> CP for Q = (23×20,00,000)/20

=> CP for Q = 23×1,00,000

=> CP for Q = Rs. 23,00,000

Answer:-

The Cost Price of the car for Q is

Rs. 23,00,000

Check :-

We have,

CP = 20,00,000

SP = 23,00,000

Profit = Selling Price - Cost Price

= 23,00,000-20,00,000

Profit= 3,00,000

Profit % = (Profit/CP)×100

=> P% = (3,00,000/20,00,000)×100

=> P% = (3/20)×100

=> P% = 0.15×100

=> Profit % = 15%

Profit for P by solding the car to Q = 15%

and

CP of Q = Rs. 23,00,000

SP of S = Rs. 25,30,000

Profit = 25,30,000 - 23,00,00

=> Profit = 2,30,000

Profit % = (2,30,000/23,00,000)×100

=> Profit % = (1/10)×100

=> Profit % = 100/10

=> Profit = 10%

Verified the given relations in the given problem.

Used formulae:-

→ If SP > CP then Profit = SP - CP

→ P% = (Profit/CP)×100

→ Selling Price = [(100+g)/100]×CP

• CP = Cost Price
• SP = Selling Price
• g = Gain or Profit