Comprehension
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur , Calcutta. In Ghosh Housing
Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person
who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur
is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33
and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur
are 32 and 117 respectively.
Question: 1
Number of persons in Dighospur who read only Ganashakti is:
Number of persons in Dighospur who read only Ganashakti is:
Show Hint
When working with set problems, use the union formula $n(A \cup B) = n(A) + n(B) - n(A \cap B)$ to find the overlap, then subtract to get "only" counts.
Updated On: Aug 5, 2025
- 121
- 83
- 79
- 127
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
From the problem data:
Total number of persons who read both newspapers in Dighospur = $200$.
In Dighospur, persons who read Ganashakti = $121$ (given in problem statement).
In Dighospur, persons who read Anand Bazar Patrika = $117$.
To find the number who read only Ganashakti, we subtract the people who read both from the total Ganashakti readers.
Only Ganashakti readers = Total Ganashakti readers $-$ Both readers.
= $121 - (200 - 117)$.
First, find “both readers” in Dighospur: Since Anand Bazar Patrika readers are $117$ and total readers of both newspapers in Dighospur are $200$, the overlap = $121 + 117 - 200 = 38$.
Thus, only Ganashakti readers in Dighospur = $121 - 38 = 83$.
Wait — rechecking: the question says "total number of persons who read these two newspapers in Dighospur is 200", which is union, not intersection.
Union formula: $G + A - \text{both} = 200$.
Substitute $G = 121$, $A = 117$: $121 + 117 - \text{both} = 200$.
$238 - \text{both} = 200 \Rightarrow \text{both} = 38$.
Only Ganashakti readers = $121 - 38 = 83$.
Hence, the correct answer is $83$.
Total number of persons who read both newspapers in Dighospur = $200$.
In Dighospur, persons who read Ganashakti = $121$ (given in problem statement).
In Dighospur, persons who read Anand Bazar Patrika = $117$.
To find the number who read only Ganashakti, we subtract the people who read both from the total Ganashakti readers.
Only Ganashakti readers = Total Ganashakti readers $-$ Both readers.
= $121 - (200 - 117)$.
First, find “both readers” in Dighospur: Since Anand Bazar Patrika readers are $117$ and total readers of both newspapers in Dighospur are $200$, the overlap = $121 + 117 - 200 = 38$.
Thus, only Ganashakti readers in Dighospur = $121 - 38 = 83$.
Wait — rechecking: the question says "total number of persons who read these two newspapers in Dighospur is 200", which is union, not intersection.
Union formula: $G + A - \text{both} = 200$.
Substitute $G = 121$, $A = 117$: $121 + 117 - \text{both} = 200$.
$238 - \text{both} = 200 \Rightarrow \text{both} = 38$.
Only Ganashakti readers = $121 - 38 = 83$.
Hence, the correct answer is $83$.
Was this answer helpful?
0
0
Question: 2
Number of persons in Aghosh Colony who read both of these newspapers is:
Number of persons in Aghosh Colony who read both of these newspapers is:
Show Hint
When you have total (union) and individual set counts, use $n(A \cap B) = n(A) + n(B) - n(A \cup B)$ directly.
Updated On: Aug 5, 2025
- 13
- 20
- 19
- 14
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
From the problem statement:
Total number of persons who read these two newspapers in Aghosh Colony = $52$ (union count).
In Aghosh Colony: Ganashakti readers = $33$, Anand Bazar Patrika readers = $32$.
Apply the union formula:
$33 + 32 - \text{both} = 52$.
$65 - \text{both} = 52$.
$\text{both} = 65 - 52 = 13$.
But wait — the problem states in Ghosh Housing Society there is no person who reads both. This applies to that society, not to Aghosh Colony data here, so no contradiction.
Thus, number of persons in Aghosh Colony who read both = $13$.
Total number of persons who read these two newspapers in Aghosh Colony = $52$ (union count).
In Aghosh Colony: Ganashakti readers = $33$, Anand Bazar Patrika readers = $32$.
Apply the union formula:
$33 + 32 - \text{both} = 52$.
$65 - \text{both} = 52$.
$\text{both} = 65 - 52 = 13$.
But wait — the problem states in Ghosh Housing Society there is no person who reads both. This applies to that society, not to Aghosh Colony data here, so no contradiction.
Thus, number of persons in Aghosh Colony who read both = $13$.
Was this answer helpful?
0
0
Question: 3
Number of persons in Aghosh Colony who read only one paper is:
Number of persons in Aghosh Colony who read only one paper is:
Show Hint
Always separate “only” counts by subtracting intersection counts from each set, then add them to get the total for “only one”.
Updated On: Aug 5, 2025
- 29
- 19
- 39
- 20
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
From Q53, number of persons who read both newspapers in Aghosh Colony = $13$.
Ganashakti readers in Aghosh Colony = $33$.
Anand Bazar Patrika readers in Aghosh Colony = $32$.
Persons who read only Ganashakti = $33 - 13 = 20$.
Persons who read only Anand Bazar Patrika = $32 - 13 = 19$.
Total persons who read only one paper = $20 + 19 = 39$.
Ganashakti readers in Aghosh Colony = $33$.
Anand Bazar Patrika readers in Aghosh Colony = $32$.
Persons who read only Ganashakti = $33 - 13 = 20$.
Persons who read only Anand Bazar Patrika = $32 - 13 = 19$.
Total persons who read only one paper = $20 + 19 = 39$.
Was this answer helpful?
0
0
Top Questions on Set Theory
- Suppose \( R_1 \) and \( R_2 \) are reflexive relations on a set \( A \). Which of the following statements is correct?
- AP PGECET - 2025
- Mathematics
- Set Theory
- Let \( A = \{1, 2, 3\} \). Which of the following is the number of distinct relations on \( A \)?
- If one card is selected from a well-shuffled deck of 52 cards, then the probability of getting an ace card is:
- Which of the following statement regarding the probability of an event is correct?
- What is the probability of getting a number 7 in a single throw of a dice?
View More Questions
Questions Asked in CAT exam
- \( 10^{68} \) is divided by 13, the remainder is is
- CAT - 2024
- Divisibility and Remainder
- ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of \(\triangle ADE\) is
- CAT - 2024
- Mensuration
- Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is
- CAT - 2024
- Time, Speed and Distance
- The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
- CAT - 2024
- Profit and Loss
- Suppose $x_1, x_2, x_3, \dots, x_{100}$ are in arithmetic progression such that $x_5 = -4$ and $2x_6 + 2x_9 = x_{11} + x_{13}$. Then, $x_{100}$ equals ?
- CAT - 2024
- Arithmetic Progression
View More Questions