Analyzing Survey Data for City Visits
We are given data from a survey of 1000 people about their visits to Delhi and Mumbai.
- Total people surveyed: 1000
- Visited Delhi (D): 600
- Visited Mumbai (M): 450
- Visited Both Delhi and Mumbai (D $\cap$ M): 250
Calculating Visitors of Only One City
To find the number of people who visited only Delhi, we subtract those who visited both cities from the total who visited Delhi.
People who visited only Delhi = Number who visited Delhi - Number who visited both
Only Delhi = $600 - 250 = 350$
Similarly, to find the number of people who visited only Mumbai, we subtract those who visited both cities from the total who visited Mumbai.
People who visited only Mumbai = Number who visited Mumbai - Number who visited both
Only Mumbai = $450 - 250 = 200$
Determining the Ratio
The question asks for the ratio of people who visited only Delhi to those who visited only Mumbai.
Ratio = (Number who visited only Delhi) : (Number who visited only Mumbai)
Ratio = $350 : 200$
To simplify the ratio, we find the greatest common divisor (GCD) of 350 and 200, which is 50.
Simplified Ratio = $\frac{350 \div 50}{200 \div 50} = \frac{7}{4}$
Therefore, the ratio is 7 : 4.
This corresponds to Option 4.
Important Questions from Set Theory and Venn Diagram (Notes)
A student is free to choose only Chemistry, only Biology or both. If out of $32$ students, Chemistry has been chosen by $16$ and Biology by $25$, then how many students have chosen Biology but not Chemistry?
- Fourteen of the students in a class are girls. Eight students in the class wear blue shirts. Two are neither girls nor wear blue shirts. Five students who wear blue shirts are girls. How many students are there in the class?
- In a group of 44 players, 26 play hockey, 24 play football and 24 play cricket. Eight of them play both hockey and football, 12 play both football and cricket, and 5 play all the three games. How many play both hockey and cricket?
- In a group of students, 30% play only cricket, 20% play only football and 10% play only basketball. 20% of the students play both football and cricket, 15% play both basketball and cricket, 10% play both football and basketball. 15 students play no games, while 5% of the students play all three games. What is the total number of students?
- Which of the following statements are true ?
A. Set A = {x : x $\in$ R and 2 < x < 3} is a null set.
B. Set A = {x : x $\in$ R and 2 < x < 4} is a singleton set.
C. Set A = {x : x $\in$ R and 1 < x < 9} is an infinite set.
D. Set A = {x : x $\in$ R and 1 < x < 9} is a finite set.
E. Set A = {a, b, c, d, e} and B = {c, d, a, e, b} are equal sets.
Choose the correct answer from the options given below :
