Aptitude - Profit and Loss - Discussion

@All.

Assume a variable x which will represent the cost price of a single ball. Since 17 balls were sold, the cost price of these 17 balls will be 17x.

The loss will be given by subtracting the selling price of 17 balls from the cost price of 17 balls. This loss is equal to the cost price of 5 balls i.e. 5x.

Using this, we can form an equation in x which can be solved to find the value of x.

If it is given that a product is sold at a loss, then this loss can be found by subtracting the selling price of the product from the cost price of the product ----> (1).

In the question, it is given that on selling 17 balls at Rs 720, there is a loss that is equal to the cost price of 5 balls. We are required to find the cost price of a single ball. Let us assume that the cost price of a single ball is x.

So, the cost price of the 17 balls will be 17x. Since the selling price is Rs 720, using formula (1), the loss is equal to,
17x – 720.

It is given in the question that this loss is equal to the cost price of 5 balls i.e. 5x.

So, we can say,
17x – 720 = 5x.
12x = 720.
x = 60.

Guys!
Check the question, how much did they sell 17 balls for?? Rs.720? Correct.

So now you know how much 17 balls cost, which is 720 bucks.
17=720.

Now,
when you sell 17 balls for 720 rupees, but the question clearly says you face a loss of '5 balls profit'.

How come? So how much does a ball exactly cost?

Lets do one thing,

Selling 17 for 720 but the loss of 5, we will minus the 5 with the 17, so,

17-5 = 12.
12 is our profit for 720. which is, 720=12!!

So,
Cost of 1 ball *12=720
Cost of 1 ball = 720/12
Cost of 1 ball = 60.

By selling 17 balls at 720, there is loss equal to CP of 5 balls,
17 balls sold means he must have purchased 17 balls.
Loss is equal to CP of 5 balls.
loss = CP - SP.
5 x CP = 17 x CP - 17 x SP,
5 CP - 17 CP = - 17 SP,
- 12 CP = - 17 SP,
12 CP = 720 ......(17 balls sold at 720 rs)
CP = 720/12,
CP = 60.

Here we found Loss.

So Equation is Loss = CP - SP (but in case of profit -> Profit = SP - CP).

Loss (CP of 5 balls) = CP (CP of 17 balls) - SP (SP of 17 balls).
(Cost of 1 Ball) * 5 = 17 - 720.
(Cost of 1 Ball) * 5 - 17 = - 720.
(Cost of 1 Ball) - 12=- 720 =720/12 =60.

So, Cost of 1 ball is Rs. 60.

@Tina.

Observing this question you find that he say.

Selling of 17 balls Rs. 720 is equal to the loss of cost prize of 5 balls. Then we find that.

Let us suppose C.P. is x.

Then C.P. of 17 balls - S.P. of 17 balls = C.P. of 5 ball.

17x-720 = 5x.

Then 12x = 720.

x = 720/12.
x = 60.

Let the C. P of 17 balls be x.

C. P of 1 ball is x/17.

S. P of 17 ball is 720.

S. P of 1 ball is 720/17.

Loss = (x/17) *5 (given loss = C. P of 5 balls).

Given in the problem.

5x/17 = x-720/17.

(formula:loss = C. P - S. P).

x = 1020.

Therefore C. P of 1 ball is x/17 = 60.

Let,
Cost price of 1 ball is x.
so, cost price of 5 balls = 5x,
and cost price of 17 balls = 17x.

In case of selling goods at loss,
Selling price+loss= Cost price.
=> 720+5x = 17x.
=> 12x = 720.
=> x = 60.

Ans: Cost price of each ball is 60.

Why it cann't be solved like this:

Loss = CP-SP
Acc to the ques
SP is given for 17 balls i.e 720
So SP of 1 ball = 720/12
let cp of 1 ball = x
loss = 5x (loss equals to the cp of 5 balls)
5x=x-720/17
5x = 17x-720/17
5x-17x= 720/17
12x = 720/17
x=???

The Cost price be 'x'
So that the cost price of 17 balls is 17x.
And the cost prince of 5 balls is 5x.
While selling 17 balls at Rs.720 he is incurring loss equal to cost price of 5 balls.
So that the equation is 17x-720 = 5x,
12x = 720
x = R.60/-

Loss = CP-SP
Acc to the ques
SP is given for 17 balls i.e 720
So SP of 1 ball = 720/12
let cp of 1 ball = x
loss = 5x (loss equals to the cp of 5 balls)
5x/17=x-720/17(loss for 17 balls)
5x/17 = (17x-720)/17
5x=17x-720
12x = 720
x=720/12
x=60