Question

a man buys two umbrellas for rupees 650 he sell one at 20% profit and other at 25% loss he get the same selling price for both find the cost price of each​

Answer 1

Answer:

Cost of the umbrella which he sold for profit = Rs.250

Cost of the umbrella which he sold for loss = Rs.400

Step-by-step explanation:

Firstly you have to build a simultaneous equation using the data given.

Since both umbrellas cost prices are different and we don't know we can assume them as x and y.

So, as their total cost is 650, we can build up our first equation as,

x + y= 650

Next,

20% means if the product costs 100 rupees then the profit will be 20 rupees. So selling price would be 100 + 20 = 120. We can write it as follows,

Cost price             Selling price

   100                              120

      x                                  s

If cost price increase so does the selling price. They are directly proportional to each other. So as this is a direct proportion to find ? you have to multiply crossly.

$x$ x 120 = 100 x s

120x = 100s

Since here you have to find the selling price s should be the subject.

So,

$\frac{120x}{100} = s$

You can simplify numerator and denominator if they have common factors.

So, 120 and 100 can be divided by 10. So the will  be left as

$\frac{12}{10}$

12 and 10 both are divisible by 2.

So,

$\frac{6x}{5}$is the selling price of the umbrella which costs x.

Since both umbrellas selling price are equal, we can take it as s.

Next,

25% loss means if the product costs 100 rupees then the loss will be 25 rupees. So selling price would be 100 - 25 = 75. We can write it as follows,

Cost price                  Selling price

     100                               75

       y                                   s

If cost price increase so does the selling price. They are directly proportional to each other. So as this is a direct proportion to find ? you have to multiply crossly.

y x 75 = 100 x s

So,

$\frac{75y}{100} = s$

75 and 100 can be further simplified by 25.

So, $\frac{3y}{4}$ is the selling price of the umbrella which costs y.

According to axiom 1, which is if

AB = BC

CD = BC

then AB=CD

So,  

$\frac{6x}{5}$ = $\frac{3y}{4}$

If you cross multiply them, then

24x = 15y

24x - 15y = 0 is the second equation.

So now we have built 2 equations we need.

x + y= 650

24x - 15y = 0

To solve a pair of simultaneous equations, at least one like term's coefficint should be equal. If not you have to make them equal.

We can make y equal in both equations by multiplying the 1st one by 15.

15 x 1st equation.

15x + 15y = 9750 (3rd Equation)

Since y has different signs in both equations (2nd and 3rd) we can add both to eliminate y.

15x + 15y + 24x - 15y = 9750 + 0

39x = 9750

x = 9750/39

  =250

So, the cost of x umbrella (which gave him profit) is Rs.250

Now we can substitute x=250 in 1st equation.

x + y = 650

250 + y = 650

y = 650 - 250 = 400

So, the cost of y umbrella (which gave him loss) is Rs.400

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