Profitable Radio

Algebra Level 3

Mahesh and Umesh both purchase a radio for the same price, and it mark up by the same amount. Mahesh first gives a discount of Rs. 20, followed by another discount of 20% on the reduced price, while Umesh first gives a discount of 20%, followed by a discount of Rs. 20.

If Mahesh's profit percent is thrice of Umesh's loss, what is Mahesh's profit (in Rs.)?

15 7 3 10

4 solutions

Nishant Kumar
Feb 10, 2014

Let the Cost price be 'Y' and the marked price be 'X' for both of them.

Then for Mahesh,

  Reduced Price after giving a discount of Rs 20 on Marked price= 'X-20'.

  Reduced Price after giving a discount of 20% on the reduced price of  'X-20'= 80% of ( X-20)
                                                                                                                                                =(0 .8X-16)

   Therefore, (0 .8X-16) will be the Selling price for Mahesh.

    Net Profit= S.P- C.P
                       = (0 .8X-16)-Y

Now for Umesh.

   Reduced Price after giving a discount of 20% on the Marked price= (80% of 'X')
                                                                                                                                = (0.8X)

   Reduced Price after giving a discount of Rs 20 on the reduced price of (0.8X) = (0.8X)-20.

    ((0.8X)-20) will be the Selling price for Umesh.       

      Net Loss= C.P- S.P
                       = Y-((0.8X)-20).

According to the question, Mahesh's profit percent is thrice of Umesh's loss. This implies,Mahesh's profit is thrice of Umesh's loss as Cost price is same for both.

                             (0 .8X-16)-Y=3(Y-((0.8X)-20))

         On solving, we get,

                               0.8X-Y = 19.                                              

       Now Mahesh's Profit = (0 .8X-16)-Y
                                               = 0.8X-Y-16
                                               =3.

Let Mahesh and Umesh buy at Rs x-K. Now let them mark the price up by K rs. So they have non discounted price for Rs.x. Now Mahesh's selling price is 0.8(x-20) and Umesh has a price 0.8x-20. Also as both of them have the same CP, we can conclude that Mahesh's profit is thrice of Umesh's profit. Now subtract Umesh's SP from Mahesh's SP. This is the profit+loss of mahesh and Umesh. Now as Umeshes loss is one third of mahesh's profit and on solving we get answer as 3.

Bala Tweakbytes - 7 years, 4 months ago

Marked up price = y (y > x)

Mahesh's profit = 4(y - 20)/5 - x = 4y/5 - x - 16 Umesh's loss = x - (4y/5 - 20) = x + 20 - 4y/5

Also, 4y/5 - x - 16 = 3(x + 20 - 4y/5) 4(4y/5 - x) = 76 => 4y/5 - x = 19

So, Mahesh's profit = 19 - 16 = Rs. 3

Mayank Devnani - 7 years, 3 months ago

Soumya Parida - 7 years, 3 months ago

Hw did u solve d equation ?...m doing ryt till d last but at last smthng z going wrong..

avilash mahapatra - 7 years, 2 months ago

Ashutosh Mahapatra
Apr 21, 2014

cute and simple lets assume bot their marked price was 100

UMESH

After discounts the price of radio is 64

MAHESH

After discounts the price becomes 60 Let the purchase the radio in x rupees since Umesh earned profit and mahesh a loss s so 64-x=3(x-60) solving gives x=61

Vaibhav Agarwal
Feb 27, 2014

Let the SP marked by both of them be x. Thus, profit for Mahesh = $\frac{4}{5}(x-20) - C.P.$ (equation 1)and loss for Umesh= $C.P. - \frac{4x}{5} - 20$ Equating them according to the question, we get $\frac{\frac{4}{5}(x-20) - C.P. }{C.P.} = 3\frac{C.P. - \frac{4x}{5} - 20 }{C.P.}$ which implies that C.P. = $\frac{4x}{5}$ - 19 Putting that in equation 1, we get the answer to be 3.

Kumar Prashant
Feb 25, 2014

This question can be easily solved if we start by assuming cost price Rs 100 and marked price Rs(100+x)

Answer can be calculated using marked pruce as 100 and cost price x and solving for both

mohi shukla - 7 years, 2 months ago

Profitable Radio

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