In such questions, it's very important to wisely choose your initial figures, here "the total number of socks". If you notice carefully, there are percentages involved in this question i.e. 40%, 60%, 25 %. Always remember the tip:
"Fractions are always better than Percentages"
This will help you in choosing your initial figures carefully.
Here, you have
40% which is nothing but
2/5 in terms of fractions.
60% is
3/5 &
25% is
1/4. If you notice the denominators of these fractions, you will come to the conclusion that the initial figure you assume i.e. the total number of socks, will be divided by 5 & 4 i.e. if you assume the total number of socks to be a multiple of 25, your calculation is going to be a lot easier.
What's the best number that you can assume which is a multiple of 25? 100, of course. So, let's start by assuming the total number of socks to be "
100S". Notice I have not taken the number of socks to be 100 but instead, I have taken it as "100S" where S is a variable. This will make sure that you are under the purview of all the mathematical rules & staying away from marking a possibly hidden wrong answer.
Why "S" though? "S" will remind me that it's Socks. Had it been Tshirts in place of socks, I would have assumed 100T.
Now, it's all about comprehending the problem statement one by one. Let's break it down.
1. 40% of all the socks are white -> "40S" socks are white.
2. The rest are black -> "60S" are black.
3. 60% socks are made of cotton -> "60S" are made of cotton.
4. The rest are made of wool -> "40S" are made of wool.
5. 25% white socks are made of cotton i.e. 1/4th of white socks are made of cotton -> 1/4th of "40S" are made of cotton i.e. 10S. Here, if 10S are made of cotton, it is implied that 30S are made of wool since there are only 2 kinds of socks i.e. cotton & wool.
Moreover, the total number of cotton socks are -> 60S (refer to 3rd point)
Out of the 60S, 10S are made white cotton socks (refer to 5th point). How many are black cotton socks then? 60S - 10S i.e.
50S & further, the rest i.e. 10S are black wool socks. This is what we are supposed to find out.
Do we have the answer yet? No, since it depends on the value of "S". If S=1, our answer is 50, if S is 1/2, our answer is 25 & so on.
What now?
There is one statement that we have not made use of. It says "20 of the black socks are made of wool." This means:
10S = 20
=> S= 2.
BINGO.
How many black socks are made of cotton?
50S i.e. 50*2 = 100.
Try the same question by changing the figures. An example is as follows:
In a shop, 28.56% socks are white and rest are black. 16.66% socks are made of cotton and rest are made of wool. 10% white socks are made of cotton and 242 of the black socks are made of wool. How many black socks are made of cotton?
Here, you will understand the importance of wisely choose your initial figures.
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