The percentage profits on three articles X, Y, and Z is 10%, 20% and 2

Question

The percentage profits on three articles X, Y, and Z is 10%, 20% and 25% and the ratio of their cost price is 1:2:4. Also, the ratio of the number of articles sold of X, Y and Z is 2:5:2. The overall profit percentage is:

A. 15
B. 17
C. 19
D. 21
E. 23

A. 15
B. 17
C. 19
D. 21
E. 23

PyjamaScientist · Answer

Let the cost price be $100, $200, and $400
Let the no. of items be 2, 5, and 2
So, the total cost price would be = 100*2 + 200*5 + 400*2 = 200 + 1000 + 800 = $2000

Now, profit on X is 10% on $200, i.e. = $20
Similarly profit on Y is 20% on $1000 = $200
Profit on Z is 25% on $800 = $200
Total profit = $420.

Total profit % =  \frac{total profit}{total cost price} * 100 
Thus, Total profit % =  \frac{420}{2000} * 100  =  21% .  (D)

sanjitscorps18 · Answer

Let CP ratios be 'a' and numbers sold ratios be 'b'

Total CP of X = 2ab
Total CP of Y = 10ab
Total CP of Z = 8b

Total CP = 20ab

Total Profit of X = 2ab/10
Total Profit of Y = 10ab/5
Total Profit of Z = 8b/4

Total Profit % = 100*(2ab/10 + 10ab/5 + 8b/4)/20ab = 21%

Option D

GMATWhizTeam · Answer

Solution:

The ratio of CP is 1:2:4. So, let the CPs be  x, 2x  and  4x .

The ratio of the number of articles is 2:5:2. So, let the number of articles be  2y, 5y  and  2y .

Thus, total CPs are  x	imes 2y=2xy, 2x	imes 5y=10xy  and  4x	imes 2y=8xy

We know the percentage profit is 10%, 20% and 25%.

So, profit on each articles are:

P_1=40 % of  2xy=\frac{xy}{2}

P_2=20 % of  10xy=2xy

P_3=25 % of  8xy=2xy

Thus, total profit  = \frac{xy}{2}+2xy+2xy=\frac{21xy}{5}

Total CP  = 2xy+10xy+8xy=20xy

Profit percent  = \frac{4.2xy}{20xy}	imes 100=21 %

Hence the right answer is    Option D   .

luisdicampo · Answer

Deconstructing the Question

The profit percentages on articles   X,\ Y,\ Z   are

10\%,\ 20\%,\ 25\%

The ratio of their cost prices is

1:2:4

The ratio of the number of articles sold is

2:5:2

We need the overall profit percentage.

This is not a simple average of  10\%,\ 20\%,\ 25\% , because both the cost prices and the quantities sold are different.

So we must use a weighted average based on total cost.

Step-by-step

Assume the cost price per article is

X=1,\ Y=2,\ Z=4

and the numbers sold are

X=2,\ Y=5,\ Z=2

Now compute total cost for each type.

For  X

2	imes1=2

For  Y

5	imes2=10

For  Z

2	imes4=8

So the total cost is

2+10+8=20

Now compute total profit from each type.

For  X

10\%	ext{ of }2=0.2

For  Y

20\%	ext{ of }10=2

For  Z

25\%	ext{ of }8=2

So total profit is

0.2+2+2=4.2

Overall profit percentage

\frac{4.2}{20}	imes100=21\%

Answer D

The percentage profits on three articles X, Y, and Z is 10%, 20% and 2

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The percentage profits on three articles X, Y, and Z is 10%, 20% and 2

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