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April 16th, 2018, 01:07 AM   #1
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Kiran bought some goods for 720 rs....

Kiran bought some goods for 720 rs. He sold one fourth of the goods at a profit of 15%. At what profit percentage should he sell the remaining goods to gain an overall profit of 21%? [Ans : 23%]

I tried:

CP = 720 /-

$\dfrac {1}{4}$ x = 15%

$\dfrac {3}{4}$ X = y %

Total profit = 21%

How can I continue from here?

Last edited by skipjack; April 16th, 2018 at 04:46 AM.
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April 16th, 2018, 03:45 AM   #2
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I am glad to see that you have tried to do this yourself first, but I am not sure I follow your logic. Rather than just writing everything out is one large arithmetic operation, it would be better to do one step at a time and explain why you are doing it.

Here is what I would do:

"Kiran bought some goods for 720 rs. He sold one forth of the goods at a profit of 15%."

Okay, 1/4 of 720 rs is 720/4= 180. 15% of that is 27 Rs.

"At what profit percentage should he sell the remaining goods to gain an overall profit of 21%?"

21% of the original 720 rs would be 151.2 Rs. Since Kiran has already made 27Rs profit, he must make 151.2- 27= 124.2 Rs profit on the remaining 720- 180= 540 Rs of goods. 124.2 on 540 is 124.2/540= 23% profit on the remaining goods.

Notice that this is a 'weighted average'. 1/4 of the goods at 15% and 3/4 at 21% is an average of (1/4)(15)+ (3/4)(23)= 21. We could have done this by solving (1/4)(15)+ (3/4)x= 21 but the way I showed first follows more directly from the information given.
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April 16th, 2018, 03:54 AM   #3
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p = profit percentage required:

720(1.21) = 180(1.15) + 540(1+p)

Solve for p: you should get .23
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April 16th, 2018, 05:05 AM   #4
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Quote:
Originally Posted by Ganesh Ujwal View Post
How can I continue from here?
Are you supposed to use alligation?
That leads directly to the answer (4*21% - 15%)/3 = 23%.
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April 16th, 2018, 07:36 AM   #5
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Quote:
Originally Posted by skipjack View Post
Are you supposed to use alligation?
No, this topic is from profit and loss.
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