Percentage Problem

N:Dure wrote:??

Total in Jan - J
Total in Feb - F
7% rejected in Jan - 7J/100
8% rejected in Feb - 8J/100
Total rejected in Jan and Feb both = 7.8 of (J + F) /100
7J + 8F = 7.8(J + F)
Solving, F = 4J
1/4

N:Dure wrote:??

I would multiply all the percentages by 10 to make the math easier. The problem then becomes:

How do we combine 70% with 80% to yield a mixture that is 78%?

This is a weighted average question. An efficient approach is alligation:

The proportion needed of each of the original percentages (70% and 80%) is the difference between the other 2 percentages.

Proportion needed of 70% = 80-78 = 2.
Proportion needed of 80% = 78-70 = 8.

Thus, the ratio needed is 2:8 = 1:4.

The correct answer is C.

Mitch,

Thank you very much for the answer. However my doubt was 1:4 for the total rejections right. That means for every 1 peice of jan rejection there has to be 4 rejections. How this can be the total ratio of production. Can you please help me understand this.

Hi Kamalkarthi,

The ratio coming out from Allegation would be
How much of J is used : How much of F is used in deriving 7.8% taken from J+ F.

To understand better:
Lets solve the same problem using the percentage of units produced.

Percentage of units produced in J= 93% (100-7)
Percentage of units produced in F =92% (100-8)
Percentage together j + f = 92.2 (100-7.8)

Hence using allegation . Ratio of J:F used = (92 - 92.2) /(92.2 -93)
= -0.2/-0.8

= 1/4
This is same as the one produced using defects percentage.
Hope this helps...