In a shipment of 120 machine parts, 5 percent were defective

SOLUTION

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%

For the two shipments combined, the percent of defective parts = (total # of defective parts)/(total # of parts)*100 = \(\frac{120*0.05+80*0.1}{120+80}*100=7%\).

Answer: B.
_________________

5% of 120 is 6
10% of 80 is 8

As the question says two shipments combined, we have two add the defective as well as total shipments.

8+6/120+80 = 15/200 = 7.5%
Answer C

There are many different ways to calculate percentages, I think the best way here can be like this
To find 10% of any no. just move one decimal point to left (10% of 120 = 12) and (10% of 80 = 8)
To find 5% of any no. just halve the above no. (5% of 120 = 12/2 = 6)

b2bt

Good logic, but I think you made a little error in your calculations.

(8+6)/(120+80) = 14/200, which leads to 7%

Answer is B.

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%


\(TotalDefectiveMachineParts = (\frac{5}{100})120 + (\frac{10}{100})80 = 6 + 8 =14\)

So, \(%\) \(OfDefectiveMachineParts= = \frac{Total Defective Machine Parts}{Total Machine Parts}=\frac{14}{200} = \frac{7}{100}=7%\)

Answer: (B)

Defective 1= 5% of 120 = 6;
Defective 2= 10% of 80 = 8;

Total Defective = 6 + 8 = 14/(120 + 80) = 14/200 = 7/100 = 7%;

Ans is (B).

Oops
I always tend to make calculation mistakes.

Out of 120 , 5% are defective.
Lets try to calculate without putting pen (read marker) to paper (read scratch pad).
10% of 120 is 12 (remove the last 0 from numerator).
Half of 12 = 6 should be 5%

and Out of 80, 10% is defective. so 8
so 8+6 = 14 out of 200 (120+80) so 14/2 should be the required answer = 7% - Option B)

Option B
Def in ship. 1: 120 *5%=6 +
Def. in ship. 2:80 * 10%=8
Total def=14
Total no.=120+80=200
%age def in total=14 *100/200=7%

Option B - 7%
5% of 120 - 6 pieces
10% of 80 - 8 pieces

If both are combined - total pieces - 200
Total defective pieces - 14
So % defective pieces - 14/200 = 7%

SOLUTION

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A) 6.5%
(B) 7.0%
(C) 7.5%
(D) 8.0%
(E) 8.5%

For the two shipments combined, the percent of defective parts = (total # of defective parts)/(total # of parts)*100 = \(\frac{120*0.05+80*0.1}{120+80}*100=7%\).

Answer: C.
_________________

for 120 shipments , 5% i.e 6 were defective .
for 80 shipments, 10% i.e 8 were defective.

Total = 200 shipments (combined) and defective =14 (combined).
question asks us 14 is what % of 200.

14/200 = x/100;
x=7% ;

Press kudos if this helps

Another solution:
Call x (%) is percent of the machine parts were defective for the two shipments combined.
120/80=(10-x)/(x-5)
=> 120 (x-5) = 80(10-x)
=> 20x = 140
=> x = 7 (%)

1. 120 x 5 = 600 = move decimal two digits left because percent = 6 parts defective from 120 shipment
2. 80 x 10 = 800 = 8 (move decimal again) parts defective
3. Find total parts = 120 + 80 = 200
4. Find total defective parts = 6 + 8 = 14
5. (14 / 200) x 100 = 7% parts defective

Answer is (B) 7.0%

In the shipment of 120 machine parts, 120 x 0.05 = 6 were defective. In the shipment of 80 machine parts, 80 x 0.1 = 8 were defective. Thus, 14/200 = 7/100 = 7% were defective overall.

Answer: B
_________________

We can solve using weighted average

1st shipment - 120 machine parts, 5% defective
2nd shipment - 80 machine parts, 10% defective

If both machine parts were equal, then answer must be 7.5%. But weight of 120 is more than 80, so answer must be closer to 5%.
We can reject C,D,E at this stage.

Y ........................... X
5%.........overall...............10%
120 ................................. 80

Multiply 120*Y = 80*X
120/80 = X/Y (where x is the distance between the overall and 10% & Y is the distance between the overall and 5% )
3/2 = X/Y
X = 3%, Y= 2%, Overall is 7%

In the first shipment of 120 machine parts, 5 percent were defective:
Number of defective parts in the first shipment = 5% of 120 = (5/100) * 120 = 6

In the second shipment of 80 machine parts, 10 percent were defective:
Number of defective parts in the second shipment = 10% of 80 = (10/100) * 80 = 8

Now, let's calculate the total number of machine parts and the total number of defective parts in the combined shipments:

Total number of machine parts = 120 + 80 = 200
Total number of defective parts = 6 + 8 = 14

To find the percentage of defective machine parts, we can calculate:
(Defective parts / Total parts) * 100

(14 / 200) * 100 = 0.07 * 100 = 7%

Therefore, the percentage of machine parts that were defective in the combined shipments is 7%, which corresponds to option (B) in the given choices.