A supermarket chain received a shipment of panettones and

Question

A supermarket chain received a shipment of panettones and recouped 100% of the cost of the shipment before Christmas by selling a fraction of them at a fixed price. After Christmas, it sold each of the remaining panettones at a price 40% lower than the pre-Christmas price. If the total revenue from the sale of the panettones was 36% greater than the cost of the shipment, the number of panettones sold after Christmas was what fraction of the number sold before Christmas?

(A) \(\frac{3}{8}\)

(B) \(\frac{3}{5}\)

(C) \(\frac{5}{8}\)

(D) \(\frac{2}{3}\)

(E) \(\frac{4}{5}\)

(A)  \frac{3}{8}

(B)  \frac{3}{5}

(C)  \frac{5}{8}

(D)  \frac{2}{3}

(E)  \frac{4}{5}

onlyPlanA · Answer

Took me 10 mins to solve this. 😭

Suppose there are x panettones and their selling price is p per panettone. And a fraction "a" of x is sold before christmas, through which the supermarket recovered the shipment cost.

So, shipment cost = selling price of ax panettones = axp

And the remaining panettones were sold at 40% discount.
So, selling price of remaining panettones = (1-a)x(0.6p)

Given that, total revenue = 1.36 * shipment cost
Hence, axp + (1-a)x(0.6)p = 1.36 axp
a + 0.6 - 0.6a = 1.36a
a = 5/8

If the number of panettones sold before christmas = 5x/8, then the number of panettones sold after christmas = 3x/8
The fraction asked = (3/8) / (5/8) = 3/8 * 8/5 = 3/5

Answer is B.

I wanted to solve it by putting in some numbers, but even then the process was lengthy.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=89322 --- Harsha GMAT-Club-Forum-q03pcaio.png

kevincan · Answer

Let’s suppose the shipment contains n panettone at a cost of c each, and that fraction f were sold before Christmas at a fixed price of p each 
We want to find (1-f)/f

Revenue before Xmas was 100% of cost of shipment :

fnp = nc

Total revenue was 36% greater than cost of shipment :

fnp + 3(1-f)np/5 = 1.36fnp

f + 3(1 -f)/5 = 34f/25
25f + 15(1-f) = 34f
15=24f
f = 5/8
1-f = 3/8
(1-f)/f = 3/5

kevincan · Answer

Express solution :

F + 0.6(1 - f) = 1.36f

0.6(1-f) = 0.36f

(1 -f)/f = 36/60= 3/5

A supermarket chain received a shipment of panettones and

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