AJWILL wrote:A shopkeeper was selling Apples, Mangoes, Oranges and Bananas. The price of one Mango was 25% more than that of one Apple, 50% more than that of one Orange and 100% more than that of one Banana. What was the percentage share of revenue from Oranges as compared to the total revenue from the above given fruits?
(1) The numbers of Bananas, Mangoes, Apples and Oranges sold were in the ratio 4:1:2:3
(2) The total revenue by selling Apples, Mangoes, Oranges and Bananas is $66
We can do this one without doing any calculations. We are told that price of mango is related to the apple, the orange and the banana as a factor. Hence we can find the ratio of revenues by selling one of each by simply converting everything in terms of the mango.
Then, to find the revenue of oranges to revenue of everything, we will only need the relative ratios of A,M,O, and B.
With this in mind, let's look at the options:
(1) The numbers of Bananas, Mangoes, Apples and Oranges sold were in the ratio 4:1:2:3
Perfect. We are given the relative ratios of all 4. Sufficient.
(2) The total revenue by selling Apples, Mangoes, Oranges and Bananas is $66
We don't care for the total revenue. There is no restriction on price of mangoes etc being an integer, hence we will have many different answers for different ratios. We need not check Insufficient.
Hence A is correct.
Here's the more detailed (albeit very time consuming) way of doing the same.
Let the price of mango be m. Then
m=1.25a => a = m/1.25
m=1.5o => o = m/1.5
m=2b => b = m/2
Statement 1:
Let the quantities of apples, mangoes etc. be A,M,O,B. Let's say the shopkeeper sells x number of mangoes.
Then:
M = x
B = 4x
A = 2x
O = 3x
Revenue from oranges = oO = m/1.5 * 3x = 2mx
Total revenue = aA+bB+mM+oO = xm(4/1.25+4/2+....). We can cancel out xm from top and bottom leaving a percentage share when we divide the two above. Sufficient.
If mangoes cost 3 dollarx, 66 = 22 mangoes in which case the percentage = 0%.
Or if we have 33 oranges (each costing 3/1.5 = 2 dollars) , percentage = 100%.
Insufficient.
I prefer the first way. Cheers!
