Amongst 100 people who were surveyed 90like Amitabha,77 like Abhishek,75 Likes Hrithik and 70 like Shahrukh.

a)Minimum number of people who like all 4.

b)Maximum number of people who like all 4.

Pls explain using minimum overlapping line method

bindu k

2 years, 5 months ago

Hi Vipul,

The answer depends on the number of people who don't like any of the four people. To maximize the number of people who like all the four persons, we have to consider the number of people who don't like any of the four persons to be as 0. In that case, the maximum number of people who like all the four would be = 70.

Similarly, the minimum number of people who like all the people would be 0, consider any number of people who doesn't like all the four people.

Hope this helps

Thanks

Mr. Lal sells only chemical Y .During the day he seels (1/11)th of the totatl quantity of the chemical with him in the morning. He observes that the total quantity of the chemical with him in the morning is 10% less than the quantity of chemical with him on the previous night. This is because the chemical Y evaporates during the course of night. Everyday he increases the selling price of the chemical by 10% with respect to the selling price of the chemical on the previous day. The cost price of the chemical is Rs 8/litre whereas on the first day he sells the chemical at Rs 10/litre

Q) If the total quantity of the chemical with him on the morning of the first day is 11000 litres, then what is the total profit made by him after he has completely sold all the chemical with him ?

Akhilesh Singh

2 years, 5 months ago

Hi

The total quantity on the morning of the first is 1100. So he will sell 1100/11 = 100 litres on first day. The price is 8 per litre so earnings would be 800

Second day he will sell 900/11 litres of chemical and earnings would be 900/11*8.8 = 900*.8 = 720

Similarly on third day the the chemical sold will be 8100/121. Hence the earnings would be 8100/121*8.8*1.1 = 648. Thus we can see that it forms a GP with a common ratio of 9/10. Thus the required sum would be

800/(1-9/10) = Rs 8000

Hope that helps.

Not able to understand the explanation of following question.

Q

An arithmetic progression of n ( n > 25 ) terms has only integers in it. The average of the first four terms is 14 and the average of the last four terms is 52. What is the common difference?

A

1

B

2

C

18

D

19

Explanation

Let the first term be a and common difference be d. The average of the first four terms is a+1.5d = 14. The average of the last 4 terms is a+(n-2.5)d = 52. Subtracting, we get, (n-4)d = 38. Since n>25, the only possibility is n-4 = 38 and d = 1.

Akhilesh Singh

2 years, 5 months ago

Hi Akshay

Let the first four terms of the AP be a, a+d, a+2d, a+3d. On finding the average, we get a+1.5d = 14

Similarly let the last 4 terms be

a + (n-1)d, a+(n-2)d + a+(n-3)d + a+(n-4)d. The average of these terms would be a + (n-2.5)d. We have been given that this average is equal to 52.

a+(n-2.5)d = 52

Subtracting the two equations we get

(n-4)d = 38

n > 25, 38 = 38*1, 19*2

Since n>25, so n can only be 42. Hence the common difference would be 1.

Hope that makes it clear.

Thanks.

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