153 persons bought three different kinds of cellular phones namely Nokia, Sony Ericsson and Motorola. The number of people who bought both Nokia and Sony Ericsson is 30. The number of people who bought both Nokia and Motorola and the number of people who bought both Sony Ericsson and Motorola is 20 and 25 respectively. The ratio of the difference between the people who bought only Nokia and only Sony Ericsson to the difference between the number of people who bought only Nokia and only Motorola is 2:3. For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia. Among the persons who bought only one kind of mobile phone, the number of persons buying Nokia was the highest.Find the maximum possible number of persons who bought Nokia.a)95b)97c)59d)96Correct answer is option 'B'. Can you explain this answer?

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153 persons bought three different kinds of cellular phones namely Nokia, Sony Ericsson and Motorola. The number of people who bought both Nokia and Sony Ericsson is 30. The number of people who bought both Nokia and Motorola and the number of people who bought both Sony Ericsson and Motorola is 20 and 25 respectively. The ratio of the difference between the people who bought only Nokia and only Sony Ericsson to the difference between the number of people who bought only Nokia and only Motorola is 2:3. For every one person who bought only Sony Ericsson, there are two persons who bought only Nokia. Among the persons who bought only one kind of mobile phone, the number of persons buying Nokia was the highest.

Find the maximum possible number of persons who bought Nokia.

a)
95
b)
97
c)
59
d)
96

Correct answer is option 'B'. Can you explain this answer?

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Most Upvoted Answer

153 persons bought three different kinds of cellular phones namely No...

To find the maximum possible number of persons who bought Nokia, let's solve the problem step by step:

Step 1: Represent the given information in a Venn diagram. We have three sets: Nokia, Sony Ericsson, and Motorola. Let's represent them as circles A, B, and C respectively.

Step 2: Let's fill in the given information. We know that the number of people who bought both Nokia and Sony Ericsson is 30, the number of people who bought both Nokia and Motorola is 20, and the number of people who bought both Sony Ericsson and Motorola is 25.

Step 3: Let's assume the number of people who bought only Nokia is x, the number of people who bought only Sony Ericsson is y, and the number of people who bought only Motorola is z.

Step 4: We are given that the ratio of the difference between the people who bought only Nokia and only Sony Ericsson to the difference between the number of people who bought only Nokia and only Motorola is 2:3. Mathematically, this can be represented as (x - y)/(x - z) = 2/3.

Step 5: We are also given that for every one person who bought only Sony Ericsson, there are two persons who bought only Nokia. Mathematically, this can be represented as y = 2x.

Step 6: Now, let's simplify the above equations. From equation 5, we can substitute y = 2x into equation 4.

(x - 2x)/(x - z) = 2/3
-x/(x - z) = 2/3
-3x = 2(x - z)
-3x = 2x - 2z
5x = 2z

Step 7: We can see that x and z are in a 5:2 ratio. Let's assume the maximum possible value for z is 2. In that case, x would be 5.

Step 8: Now, let's find the value of y using equation 5.
y = 2x
y = 2(5)
y = 10

Step 9: Now, let's find the total number of people who bought Nokia.
Total = x + (people who bought both Nokia and Sony Ericsson) + (people who bought both Nokia and Motorola)
Total = 5 + 30 + 20
Total = 55

Therefore, the maximum possible number of persons who bought Nokia is 55, which is option B.

Answered by Wizius Careers · View profile

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Community Answer

153 persons bought three different kinds of cellular phones namely No...

In the following venn diagram N, S and M stands for Nokia, Sony Ericsson and Motorola respectively.

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Given that (a − c) : (a − b) = 2 : 3 and a : c = 2 : 1. Let us assume that a = 4K, b = K and c = 2K where K is a constant

Now, 4K + 50 − x + 2K + 25 − x + K = 153

K=78+2x

The fallowing are the possible values of K and x that satisfy the above equation: (K = 12, x = 3) ; (K = 14, x = 10) and (K = 16 and x = 17)

Minimum possible number of persons who bought Nokia a + (30 - x) + x + ( 20 - x) = 50 + 4K - x = 50 + (4 x 16) - 17 = 97.

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