According to a certain estimation, the total number of black cats is 2

Question

According to a certain estimation, the total number of black cats is 25% greater than the number of black male cats, and the number of all female cats is 5 times the number of black female cats. If the male cats are 50% of all cats, then what percent of male cats are black?

A. 10
B. 20
C. 40
D. 50
E. 80

A. 10
B. 20
C. 40
D. 50
E. 80

JoyeetaChak · Answer

Let total cats be 100
Hence, total female cats = 50 and total male cats = 50

Let the male black cats be defined as k

Thus total black cats = 1.25k
Non Black male = (50-k)
Non Black Female = 40

Total Non Black cats = (100-1.25k)

Find attached for matrix formed.

Based on the equation,

100-1.25k = (50-k) + 40
or, k = 40

Required percentage = (k/50) * 100
 = 80%

IMO E

Abhibarua · Answer

Let the number of black male cats (BM) be 'x'. So the number of total black cats (TB) will be 1.25x. And the number of black female (BF) cats will be 1.25x - x = 0.25x.

Since the number of all female cats (TF) is 5 times the number of black female cats (BF), TF = 5*0.25x = 1.25x.

If the male cats are 50% of all cats, the other 50% must be female cats (TF). In other words, total male cats (TM) = total female cats (TF) = 1.25x.

Now, BM = x, and TM = 1.25x. So BM/ TM = 1/1.25 = 4/5 = 80% (OPTION: E)

Fdambro294 · Answer

(Total Black Cats) are composed of:

Black and Male

+

Black and Female

If we let the number of (Black and Male) = X

The the (Total Black) = X + 25%X = 125%X = (5/4)X

Total Black = (Black and Male) + (Black and Female)

(5/4)X = (X) + (Black and Female)

(Black and Female) = (1/4)X

Then we are told that the (Total Female) is 5 times the number of (Black and Female), which we found as = (1/4)X

Further, if the (Total Male) cats make up 50% ———-> then the (Total Female) make up 50%

Total Female = 50% = 5 * (Black and Female)

50% = 5 * (1/4)X

50% = (5/4)X ———-> which is the same expression we found for the (Total Black)

If (Total Black) = 50% = (5/4)X

Then (Black and Male) = X = (4/4)X = 40%

Finally:

(Black and Male) / (Total Black) = (40%) / (50%) = 80/100

80%

Posted from my mobile device

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According to a certain estimation, the total number of black cats is 2

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According to a certain estimation, the total number of black cats is 2

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