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A grocery store bought some mangoes at a rate of 5 [#permalink]
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25 Jan 2014, 05:54
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A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes? A. 1:4 B. 1:5 C. 2:3 D. 1:2 E. 2:5
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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25 Jan 2014, 10:43
guerrero25 wrote: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
A. 1:4 B. 1:5 C. 2:3 D. 1:2 E. 2:5 The cost price of a mango = 1/5 dollars. The selling price of a mango from the first stack = 1/3 dollars > the profit from one mango = 1/3  1/5 = 2/15 = 4/30 dollars. The selling price of a mango from the second stack = 1/6 dollars > the loss from one mango = 1/5  1/6 = 1/30 dollars. The profit from one mango from the first stack is 4 times the loss from one mango from the second stack. Thus, to break even, 4 times as many mangoes must be sold at loss as at profit. The ratio = 1:4. For example, if one one mango was sold at a profit of 4/30 dollars, 4 mangoes must be sold at a loss of 1/30 dollars to break even. Answer: A.
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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04 Mar 2014, 04:38
rate of 3 for a dollar means 3 mangoes in 1 dollar Say x mangoes are sold for rate of 3 for a dollar means price of 1 mango = 1/3 & price of x mangoes = 1/3 . x .................. (1) y mangoes are sold for rate of 6 for a dollar means price of 1 mango = 1/6 & price of y mangoes = 1/6 . y ......................... (2) Total selling price = 1/3 x + 1/6 y ........................ (3) Adding (1) & (2) Total Mangoes procured = (x+y); rate of 5 for a dollar means 5 mangoes in 1 dollar Total Cost Price = 1/5 . (x+y) ........................... (4) Equating (3) & (4) we get x:y = 1:4 = Answer = A
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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22 Sep 2014, 01:40
guerrero25 wrote: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
A. 1:4 B. 1:5 C. 2:3 D. 1:2 E. 2:5 Lets say he bought mangoes worth '$z' so total no. of mangoes = 5z he made a stash of 3 mangoes to be sold at $x, total no. of mangoes in this stash = 3x and a second stash of 6 mangoes to be sold at $y total no. of mangoes in this stash = 6y so we get two equations z = x+ y & 5z = 3x+ 6y solving these two we get x/y = 1/2 (WHICH IS PRICE) for no. of mangoes i.e. 3x/6y = x/2y = 1/4 OA : A



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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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22 Sep 2014, 06:21
PareshGmat wrote: rate of 3 for a dollar means 3 mangoes in 1 dollar
Say x mangoes are sold for rate of 3 for a dollar means price of 1 mango = 1/3 & price of x mangoes = 1/3 . x .................. (1)
y mangoes are sold for rate of 6 for a dollar means price of 1 mango = 1/6 & price of y mangoes = 1/6 . y ......................... (2)
Total selling price = 1/3 x + 1/6 y ........................ (3) Adding (1) & (2)
Total Mangoes procured = (x+y); rate of 5 for a dollar means 5 mangoes in 1 dollar Total Cost Price = 1/5 . (x+y) ........................... (4)
Equating (3) & (4)
we get x:y = 1:4 = Answer = A nice explanation. When equating (3) and(4) 1/3 x + 1/6 y = 1/5 . (x+y) (2y+x)/6xy = 1/(5x+5y) 5(2y+x)(x+y)=6xy 10y^2 + 5x^2 + 9xy = 0 i got stuck here
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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23 Sep 2014, 01:19
him1985 wrote: PareshGmat wrote: rate of 3 for a dollar means 3 mangoes in 1 dollar
Say x mangoes are sold for rate of 3 for a dollar means price of 1 mango = 1/3 & price of x mangoes = 1/3 . x .................. (1)
y mangoes are sold for rate of 6 for a dollar means price of 1 mango = 1/6 & price of y mangoes = 1/6 . y ......................... (2)
Total selling price = 1/3 x + 1/6 y ........................ (3) Adding (1) & (2)
Total Mangoes procured = (x+y); rate of 5 for a dollar means 5 mangoes in 1 dollar Total Cost Price = 1/5 . (x+y) ........................... (4)
Equating (3) & (4)
we get x:y = 1:4 = Answer = A nice explanation. When equating (3) and(4) 1/3 x + 1/6 y = 1/5 . (x+y) (2y+x)/6xy = 1/(5x+5y) 5(2y+x)(x+y)=6xy 10y^2 + 5x^2 + 9xy = 0 i got stuck here Hello buddy. I think you put wrong equation. Assume we have total mangoes = T Pack 1 has x mangoes Pack 2 has y mangoes => T = x + y Cost = T/5 = (x +y)/5 [you put 5/(x+y)]Revenue pack 1 = x/3 [you put 3/x]Revenue pack 2 = y/6 [you put 6/y]=> (x+y)/5 = x/3 +y/6 => 4x = y => Ratio 1:4 A is correct.
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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23 Sep 2014, 03:03
Please explain whats the issue with my approach. Break even means no profit no loss. 3 mangoes bought at 5$ per mango = 15$ cost price. 1 mango sold at 3$ per mango = 3 $ 2 Mangoes sold at 6$ per mango = 12 $ Ratio should be 1:2
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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23 Sep 2014, 06:36
aadikamagic wrote: Please explain whats the issue with my approach. Break even means no profit no loss.
3 mangoes bought at 5$ per mango = 15$ cost price. 1 mango sold at 3$ per mango = 3 $ 2 Mangoes sold at 6$ per mango = 12 $
Ratio should be 1:2 Please reread the question. A grocery store bought some mangoes at a rate of 5 for a dollar > 5 mangoes for a dollar > the cost price of a mango = 1/5 dollars. One stack was sold at a rate of 3 for a dollar (3 mangoes for 1 dollar) > the selling price of a mango from the first stack = 1/3 dollars. Another stack was sold at a rate of 6 for a dollar (6 mangoes for 1 dollar) > he selling price of a mango from the second stack = 1/6 dollars
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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23 Sep 2014, 06:59
aadikamagic wrote: Please explain whats the issue with my approach. Break even means no profit no loss.
3 mangoes bought at 5$ per mango = 15$ cost price. 1 mango sold at 3$ per mango = 3 $ 2 Mangoes sold at 6$ per mango = 12 $
Ratio should be 1:2 Please reread the Question it says he bought 5 mangoes for $1 and sold at 3 mangoes for $1 sold at 6 mangoes for $1



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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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26 Jun 2016, 02:46
Each mango from the first stack sold generates (1/31/5) = 2/15 profit Each mango from the second stack sold generates (1/51/6) = 1/30 loss Since 2/15 / (1/30) = 4, to break even, we need to sell 1 mango from the first stack for each 4 sold from the second stack. Answer choice A.
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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27 Jun 2016, 19:04
1/3*x+1/6*y=1/5(x+y) x/y=1/4



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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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27 Jun 2016, 21:17
guerrero25 wrote: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
A. 1:4 B. 1:5 C. 2:3 D. 1:2 E. 2:5 To avoid fractions, assume there were 45 mangoes. So the store bought them for 45/5 = 9 dollars. To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these. 45 split in the ratio 1:4 gives 9 and 36. 9 mangoes split into 3 mangoes each will give $3. 36 mangoes split into 6 mangoes each will give $6. They add up to $9 so we have hit the right answer. Answer (A)
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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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10 Aug 2017, 14:57
Resolved it through primes some mangoes at a rate of 5 for a dollar  so 5 is the known prime factor one stack was sold at a rate of 3 for a dollar  so 3 is the known prime factor and the other at a rate of 6 for a dollar  so 2 and 3 are prime factors
total (avoiding duplicating 3)  5 * 2 * 3 = 30 so if 30 mangoes were bought then the dollar amount is 6
how we can divide 30 in 2 stacks by keeping the same total dollar amount 2*3 = 2$ and 6 * 4 = 4$
Then ration between first stack and the second one: 6 mangoes / 24 mangoes = 1:4



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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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14 Feb 2018, 12:06
Let initial number of mangoes = 60 cost of 60 mangoes = 60/5 = 12 stack 1 = x mangoes, stack 2 = y mangoes x + y = 60 (1) store broke even, 12 = (x/3) + (y/6) (2) solving two equations x = 12, y = 48, ratio of x:y = 1:4 > (A)



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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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14 Feb 2018, 13:16
5 mangoes @ 1/5$, x mangoes @ 1/3$ and y mangoes @ 1/6$. Also, x + y=5. Therefore, 5*1/5= x*1/3 + y*1/6 to breakeven. Hence, x=3y/2 & x+y=5, thus, 5y=3y/2, y=4. x=1.
B.



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Re: A grocery store bought some mangoes at a rate of 5 [#permalink]
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14 Feb 2018, 17:48
guerrero25 wrote: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
A. 1:4 B. 1:5 C. 2:3 D. 1:2 E. 2:5 let x=number of 3 for a dollar mangoes sold y=number of 6 for a dollar mangoes sold x/3+y/6=(x+y)/5 x/y=1/4 x:y=1:4 A




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