Read the following information carefully and answer the 4 questions.A survey was conducted among 200 users of laptops of different companies. It was found that 160 use laptops of SONY, 100 use laptops of HP and 90 use laptops of TOSHIBA. 20 use laptops of all the three companies and each one uses laptops of at least one of the three companies.Q3. If 60 uses TOSHIBA and SONY only, then how many uses only HP ?Question 20Answera.30b.50c.25d.40
Question
Read the following information carefully and answer the 4 questions.A survey was conducted among 200 users of laptops of different companies. It was found that 160 use laptops of SONY, 100 use laptops of HP and 90 use laptops of TOSHIBA. 20 use laptops of all the three companies and each one uses laptops of at least one of the three companies.Q3. If 60 uses TOSHIBA and SONY only, then how many uses only HP ?Question 20Answera.30b.50c.25d.40
Solution
To solve this problem, we need to use the principle of inclusion and exclusion.
First, let's add up all the users: SONY users = 160 HP users = 100 TOSHIBA users = 90
This gives us a total of 350 users. However, we know that there are only 200 users, which means some users are being counted more than once.
We know that 20 users use all three brands, so we subtract this from our total: 350 users - 20 users = 330 users
We also know that 60 users use only TOSHIBA and SONY. These users are being counted in both the TOSHIBA and SONY totals, so we subtract them as well: 330 users - 60 users = 270 users
Now, we have the number of users who use only one or two brands. Since each user uses at least one brand, the number of users who use only HP is the total number of users minus the number of users who use one or two other brands: 200 users - 270 users = -70 users
However, it's not possible to have a negative number of users. This means that some users are still being counted more than once.
The only way this can happen is if some users are using both HP and one of the other brands. Since we've already accounted for users who use all three brands and users who use only TOSHIBA and SONY, the remaining users must use both HP and SONY or HP and TOSHIBA.
Since we don't have information on how many users use both HP and SONY or HP and TOSHIBA, we can't determine the exact number of users who use only HP. Therefore, the answer is not given in the options.
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