UPSC Insta–DART (Daily Aptitude and Reasoning Test) 14 & 15 Oct 2025

Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.

Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).

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• Question 1 of 10 1. Question In a company, 70% employees work in Sales. An employee who does not work in Sales works in Support. Every Support employee works night shift. Which of the following conclusions cannot be drawn from the above data? 30% of the employees work night shift. No Sales employee works night shift. Sales employees do not work in Support. Select the correct answer using the code given below: (a) 1 and 2 only (b) 2 and 3 only (c) 1 and 3 only (d) 1, 2 and 3 Correct Answer – D Solution: Given that, 70% work in Sales. Anyone not in Sales works in Support. Every Support employee works night shift. Now, Saying exactly 30% work night shift cannot be concluded. At least the non-Sales 30% are on night shift, but some Sales employees might also work night shift. Nothing says Sales staff cannot be on night shift. Cannot be concluded. It is not stated that roles are exclusive. We cannot conclude Sales employees do not work in Support. Cannot be concluded. Hence option (d) is correct. Incorrect Answer – D Solution: Given that, 70% work in Sales. Anyone not in Sales works in Support. Every Support employee works night shift. Now, Saying exactly 30% work night shift cannot be concluded. At least the non-Sales 30% are on night shift, but some Sales employees might also work night shift. Nothing says Sales staff cannot be on night shift. Cannot be concluded. It is not stated that roles are exclusive. We cannot conclude Sales employees do not work in Support. Cannot be concluded. Hence option (d) is correct.

#### 1. Question

In a company, 70% employees work in Sales. An employee who does not work in Sales works in Support. Every Support employee works night shift. Which of the following conclusions cannot be drawn from the above data?

• 30% of the employees work night shift.

• No Sales employee works night shift.

• Sales employees do not work in Support.

Select the correct answer using the code given below:

• (a) 1 and 2 only

• (b) 2 and 3 only

• (c) 1 and 3 only

• (d) 1, 2 and 3

Answer – D Solution:

Given that,

70% work in Sales. Anyone not in Sales works in Support. Every Support employee works night shift.

• Saying exactly 30% work night shift cannot be concluded. At least the non-Sales 30% are on night shift, but some Sales employees might also work night shift.

• Nothing says Sales staff cannot be on night shift. Cannot be concluded.

• It is not stated that roles are exclusive. We cannot conclude Sales employees do not work in Support. Cannot be concluded.

Hence option (d) is correct.

Answer – D Solution:

Given that,

70% work in Sales. Anyone not in Sales works in Support. Every Support employee works night shift.

• Saying exactly 30% work night shift cannot be concluded. At least the non-Sales 30% are on night shift, but some Sales employees might also work night shift.

• Nothing says Sales staff cannot be on night shift. Cannot be concluded.

• It is not stated that roles are exclusive. We cannot conclude Sales employees do not work in Support. Cannot be concluded.

Hence option (d) is correct.

• Question 2 of 10 2. Question There are 80 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. 12 students can speak both English and Hindi. If the number of students who can speak English is 50, then how many students can speak Hindi, how many can speak only Hindi and how many can speak only English? (a) 48, 36 and 14 respectively. (b) 44, 32 and 18 respectively. (c) 42, 30 and 38 respectively. (d) 40, 28 and 22 respectively. Correct Answer – C Solution: Given that, There are 80 students in total. 12 students can speak both English and Hindi. Number of students who can speak English is 50. Now, Number of students who can speak only English = 50 − 12 = 38 Number of students who can speak Hindi = 80 − 38 = 42 Number of students who can speak only Hindi = 42 − 12 = 30 Hence option (c) is correct. Incorrect Answer – C Solution: Given that, There are 80 students in total. 12 students can speak both English and Hindi. Number of students who can speak English is 50. Now, Number of students who can speak only English = 50 − 12 = 38 Number of students who can speak Hindi = 80 − 38 = 42 Number of students who can speak only Hindi = 42 − 12 = 30 Hence option (c) is correct.

#### 2. Question

There are 80 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. 12 students can speak both English and Hindi. If the number of students who can speak English is 50, then how many students can speak Hindi, how many can speak only Hindi and how many can speak only English?

• (a) 48, 36 and 14 respectively.

• (b) 44, 32 and 18 respectively.

• (c) 42, 30 and 38 respectively.

• (d) 40, 28 and 22 respectively.

Answer – C Solution:

Given that,

There are 80 students in total. 12 students can speak both English and Hindi. Number of students who can speak English is 50.

Number of students who can speak only English = 50 − 12 = 38 Number of students who can speak Hindi = 80 − 38 = 42 Number of students who can speak only Hindi = 42 − 12 = 30

Hence option (c) is correct.

Answer – C Solution:

Given that,

There are 80 students in total. 12 students can speak both English and Hindi. Number of students who can speak English is 50.

Number of students who can speak only English = 50 − 12 = 38 Number of students who can speak Hindi = 80 − 38 = 42 Number of students who can speak only Hindi = 42 − 12 = 30

Hence option (c) is correct.

• Question 3 of 10 3. Question Neha has Rs. 15,000 with her and she wants to buy a mobile handset; but she finds that she has only 60% of the amount required to buy the handset. Therefore, she borrows Rs. 10,000 from a friend. Then (a) Neha still does not have enough amount to buy the handset. (b) Neha has exactly the same amount as required to buy the handset. (c) Neha has enough amount to buy the handset and she will have Rs. 500 with her after buying the handset. (d) Neha has enough amount to buy the handset and she will have Rs. 1,000 with her after buying the handset. Correct Answer- B Solution: Given that, Amount with Neha = Rs. 15,000 This is 60% of the handset price Amount borrowed = Rs. 10,000 Now, Let price of handset be H 15,000 = 60% of H H = (15,000 x 100) / 60 = Rs. 25,000 Total amount with Neha after borrowing = 15,000 + 10,000 = Rs. 25,000 Hence, Neha has exactly the same amount as required to buy the handset. Hence option (b) is correct Incorrect Answer- B Solution: Given that, Amount with Neha = Rs. 15,000 This is 60% of the handset price Amount borrowed = Rs. 10,000 Now, Let price of handset be H 15,000 = 60% of H H = (15,000 x 100) / 60 = Rs. 25,000 Total amount with Neha after borrowing = 15,000 + 10,000 = Rs. 25,000 Hence, Neha has exactly the same amount as required to buy the handset. Hence option (b) is correct

#### 3. Question

Neha has Rs. 15,000 with her and she wants to buy a mobile handset; but she finds that she has only 60% of the amount required to buy the handset. Therefore, she borrows Rs. 10,000 from a friend. Then

• (a) Neha still does not have enough amount to buy the handset.

• (b) Neha has exactly the same amount as required to buy the handset.

• (c) Neha has enough amount to buy the handset and she will have Rs. 500 with her after buying the handset.

• (d) Neha has enough amount to buy the handset and she will have Rs. 1,000 with her after buying the handset.

Answer- B Solution:

Given that,

Amount with Neha = Rs. 15,000 This is 60% of the handset price Amount borrowed = Rs. 10,000

Let price of handset be H 15,000 = 60% of H H = (15,000 x 100) / 60 = Rs. 25,000

Total amount with Neha after borrowing = 15,000 + 10,000 = Rs. 25,000

Hence, Neha has exactly the same amount as required to buy the handset. Hence option (b) is correct

Answer- B Solution:

Given that,

Amount with Neha = Rs. 15,000 This is 60% of the handset price Amount borrowed = Rs. 10,000

Let price of handset be H 15,000 = 60% of H H = (15,000 x 100) / 60 = Rs. 25,000

Total amount with Neha after borrowing = 15,000 + 10,000 = Rs. 25,000

Hence, Neha has exactly the same amount as required to buy the handset. Hence option (b) is correct

• Question 4 of 10 4. Question In a city, 10% of households earn less than Rs. 50,000 per year, 8% households earn more than Rs. 2,50,000 per year, 30% households earn more than Rs. 1,50,000 per year and 1800 households earn between Rs. 50,000 and Rs. 1,50,000 per year. How many households earn between Rs. 1,50,000 and Rs. 2,50,000 per year? (a) 600 (b) 620 (c) 660 (d) 680 Correct Answer – C Solution: Given that, 10% earn below Rs. 50,000 8% earn above Rs. 2,50,000 30% earn above Rs. 1,50,000 1800 households are between Rs. 50,000 and Rs. 1,50,000 Now, Income group from Rs. 1,50,000 to Rs. 2,50,000 = 30% − 8% = 22% Percentage from Rs. 50,000 to Rs. 1,50,000 = 100 − (10 + 22 + 8) = 60% Total households = 1800 × (100/60) = 3000 Households between Rs. 1,50,000 and Rs. 2,50,000 = 22% of 3000 = 660 Hence option (c) is correct Incorrect Answer – C Solution: Given that, 10% earn below Rs. 50,000 8% earn above Rs. 2,50,000 30% earn above Rs. 1,50,000 1800 households are between Rs. 50,000 and Rs. 1,50,000 Now, Income group from Rs. 1,50,000 to Rs. 2,50,000 = 30% − 8% = 22% Percentage from Rs. 50,000 to Rs. 1,50,000 = 100 − (10 + 22 + 8) = 60% Total households = 1800 × (100/60) = 3000 Households between Rs. 1,50,000 and Rs. 2,50,000 = 22% of 3000 = 660 Hence option (c) is correct

#### 4. Question

In a city, 10% of households earn less than Rs. 50,000 per year, 8% households earn more than Rs. 2,50,000 per year, 30% households earn more than Rs. 1,50,000 per year and 1800 households earn between Rs. 50,000 and Rs. 1,50,000 per year. How many households earn between Rs. 1,50,000 and Rs. 2,50,000 per year?

Answer – C Solution:

Given that,

10% earn below Rs. 50,000 8% earn above Rs. 2,50,000 30% earn above Rs. 1,50,000 1800 households are between Rs. 50,000 and Rs. 1,50,000

Income group from Rs. 1,50,000 to Rs. 2,50,000 = 30% − 8% = 22% Percentage from Rs. 50,000 to Rs. 1,50,000 = 100 − (10 + 22 + 8) = 60%

Total households = 1800 × (100/60) = 3000

Households between Rs. 1,50,000 and Rs. 2,50,000 = 22% of 3000 = 660

Hence option (c) is correct

Answer – C Solution:

Given that,

10% earn below Rs. 50,000 8% earn above Rs. 2,50,000 30% earn above Rs. 1,50,000 1800 households are between Rs. 50,000 and Rs. 1,50,000

Income group from Rs. 1,50,000 to Rs. 2,50,000 = 30% − 8% = 22% Percentage from Rs. 50,000 to Rs. 1,50,000 = 100 − (10 + 22 + 8) = 60%

Total households = 1800 × (100/60) = 3000

Households between Rs. 1,50,000 and Rs. 2,50,000 = 22% of 3000 = 660

Hence option (c) is correct

• Question 5 of 10 5. Question A and B decide to travel from place X to place Y by bus. A has Rs. 8 with him and he finds that it is 40% of the bus fare for two persons. B finds that he has Rs. 7 with him and hands it over to A. In this context, which one of the following statements is correct? (a) Now the money A has just enough to buy two tickets. (b) A still needs Rs. 5 for buying the tickets. (c) After buying the two tickets A will be left with Rs. 2. (d) The money A now has is still not sufficient to buy two tickets. Correct Answer- B Solution: Given that, A has Rs. 8 which is 40% of the fare for two persons. B has Rs. 7 and gives it to A. Now, Let total fare for two persons be Rs. F. 40% of F = 8 ⇒ F = (8 × 100) / 40 = Rs. 20. Total money with A after B’s contribution = 8 + 7 = Rs. 15. Shortfall = 20 − 15 = Rs. 5. Hence option (b) is correct. Incorrect Answer- B Solution: Given that, A has Rs. 8 which is 40% of the fare for two persons. B has Rs. 7 and gives it to A. Now, Let total fare for two persons be Rs. F. 40% of F = 8 ⇒ F = (8 × 100) / 40 = Rs. 20. Total money with A after B’s contribution = 8 + 7 = Rs. 15. Shortfall = 20 − 15 = Rs. 5. Hence option (b) is correct.

#### 5. Question

A and B decide to travel from place X to place Y by bus. A has Rs. 8 with him and he finds that it is 40% of the bus fare for two persons. B finds that he has Rs. 7 with him and hands it over to A. In this context, which one of the following statements is correct?

• (a) Now the money A has just enough to buy two tickets.

• (b) A still needs Rs. 5 for buying the tickets.

• (c) After buying the two tickets A will be left with Rs. 2.

• (d) The money A now has is still not sufficient to buy two tickets.

Answer- B Solution:

Given that,

A has Rs. 8 which is 40% of the fare for two persons. B has Rs. 7 and gives it to A.

Let total fare for two persons be Rs. F. 40% of F = 8 ⇒ F = (8 × 100) / 40 = Rs. 20. Total money with A after B’s contribution = 8 + 7 = Rs. 15. Shortfall = 20 − 15 = Rs. 5.

Hence option (b) is correct.

Answer- B Solution:

Given that,

A has Rs. 8 which is 40% of the fare for two persons. B has Rs. 7 and gives it to A.

Let total fare for two persons be Rs. F. 40% of F = 8 ⇒ F = (8 × 100) / 40 = Rs. 20. Total money with A after B’s contribution = 8 + 7 = Rs. 15. Shortfall = 20 − 15 = Rs. 5.

Hence option (b) is correct.

• Question 6 of 10 6. Question A, B, C, D, E and F are six members of a family. D is the spouse of B. A is the son of D. E is the spouse of A. C is the daughter of A. F is the brother of B. There are two couples in the family. Which one of the following is correct? (a) B is the grandparent of C (b) E is the mother-in-law of D (c) C is the niece of F (d) D is the mother of A Correct Answer – A Solution: Given that, D is the spouse of B, so B and D are a couple. A is the son of D, therefore A is child of D (and B). A is male. E is the spouse of A, so A and E are the second couple. C is the daughter of A, so C is child of A (and E). F is the brother of B, so F is sibling of C’s grandparent. Now, B is a parent of A and grandparent of C. So statement (a) is correct. E is the spouse of A (child of B and D), so E is daughter-in-law of B and D, not mother-in-law. So (b) is not correct. C is grand-niece of F (since F is sibling of C’s grandparent), not niece. So (c) is not correct. D could be father or mother of A; gender of D is not given. So (d) is not necessarily correct. Hence option (a) is correct. Incorrect Answer – A Solution: Given that, D is the spouse of B, so B and D are a couple. A is the son of D, therefore A is child of D (and B). A is male. E is the spouse of A, so A and E are the second couple. C is the daughter of A, so C is child of A (and E). F is the brother of B, so F is sibling of C’s grandparent. Now, B is a parent of A and grandparent of C. So statement (a) is correct. E is the spouse of A (child of B and D), so E is daughter-in-law of B and D, not mother-in-law. So (b) is not correct. C is grand-niece of F (since F is sibling of C’s grandparent), not niece. So (c) is not correct. D could be father or mother of A; gender of D is not given. So (d) is not necessarily correct. Hence option (a) is correct.

#### 6. Question

A, B, C, D, E and F are six members of a family. D is the spouse of B. A is the son of D. E is the spouse of A. C is the daughter of A. F is the brother of B. There are two couples in the family. Which one of the following is correct?

• (a) B is the grandparent of C

• (b) E is the mother-in-law of D

• (c) C is the niece of F

• (d) D is the mother of A

Answer – A

Given that,

D is the spouse of B, so B and D are a couple. A is the son of D, therefore A is child of D (and B). A is male. E is the spouse of A, so A and E are the second couple. C is the daughter of A, so C is child of A (and E). F is the brother of B, so F is sibling of C’s grandparent.

B is a parent of A and grandparent of C. So statement (a) is correct. E is the spouse of A (child of B and D), so E is daughter-in-law of B and D, not mother-in-law. So (b) is not correct. C is grand-niece of F (since F is sibling of C’s grandparent), not niece. So (c) is not correct. D could be father or mother of A; gender of D is not given. So (d) is not necessarily correct.

Hence option (a) is correct.

Answer – A

Given that,

Hence option (a) is correct.

• Question 7 of 10 7. Question If only Sundays are taken as holidays for an office (no Saturday holiday), what would be the minimum number of possible working days of any month of any year? (a) 24 (b) 25 (c) 26 (d) 27 Correct Answer – A Solution: Given that, Only Sundays are holidays. Now, To minimise working days, pick a month with the fewest total days but as many Sundays as possible. February (non-leap) has 28 days with 4 Sundays → working days = 28 − 4 = 24. February (leap) can have 29 days with 5 Sundays → working days = 29 − 5 = 24. Thus the minimum possible is 24. Hence option (a) is correct. Incorrect Answer – A Solution: Given that, Only Sundays are holidays. Now, To minimise working days, pick a month with the fewest total days but as many Sundays as possible. February (non-leap) has 28 days with 4 Sundays → working days = 28 − 4 = 24. February (leap) can have 29 days with 5 Sundays → working days = 29 − 5 = 24. Thus the minimum possible is 24. Hence option (a) is correct.

#### 7. Question

If only Sundays are taken as holidays for an office (no Saturday holiday), what would be the minimum number of possible working days of any month of any year?

Answer – A Solution:

Given that,

Only Sundays are holidays.

To minimise working days, pick a month with the fewest total days but as many Sundays as possible. February (non-leap) has 28 days with 4 Sundays → working days = 28 − 4 = 24. February (leap) can have 29 days with 5 Sundays → working days = 29 − 5 = 24. Thus the minimum possible is 24.

Hence option (a) is correct.

Answer – A Solution:

Given that,

Only Sundays are holidays.

Hence option (a) is correct.

• Question 8 of 10 8. Question Question is given followed by two Statements I and II. Consider the Question and the Statements. Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q. Question: What is the difference of their ages? Statement-I: The age of P is greater than the age of Q. Statement-II: The sum of their ages is 44/27 times their difference. Which one of the following is correct in respect of the above Question and the Statements? (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone (b) The Question can be answered by using either Statement alone (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone (d) The Question cannot be answered even by using both the Statements together Correct Answer – A Solution: Given that, Age of P and Q is less than 100 years but more than 10 years. Digits of P when interchanged the number represents Q. Statement I: The age of P is greater than the age of Q. Statement II: The sum of their ages is 44/27 times their difference. Now, Let P = 10x + y and Q = 10y + x. Statement I: 10x + y > 10y + x ⇒ x > y, but the difference cannot be determined. Hence statement I is insufficient. Statement II: 11x + 11y = (44/27)(9x − 9y) 11(x + y) = (44/3)(x − y) Multiply by 3: 33x + 33y = 44x − 44y ⇒ 11x = 77y ⇒ x = 7y. With 1 ≤ y ≤ 9 and x ≤ 9, the only possibility is y = 1, x = 7. So P = 71 and Q = 17. Difference = 71 − 17 = 54. Hence statement II is sufficient to answer the question. Therefore option (a) is correct. Incorrect Answer – A Solution: Given that, Age of P and Q is less than 100 years but more than 10 years. Digits of P when interchanged the number represents Q. Statement I: The age of P is greater than the age of Q. Statement II: The sum of their ages is 44/27 times their difference. Now, Let P = 10x + y and Q = 10y + x. Statement I: 10x + y > 10y + x ⇒ x > y, but the difference cannot be determined. Hence statement I is insufficient. Statement II: 11x + 11y = (44/27)(9x − 9y) 11(x + y) = (44/3)(x − y) Multiply by 3: 33x + 33y = 44x − 44y ⇒ 11x = 77y ⇒ x = 7y. With 1 ≤ y ≤ 9 and x ≤ 9, the only possibility is y = 1, x = 7. So P = 71 and Q = 17. Difference = 71 − 17 = 54. Hence statement II is sufficient to answer the question. Therefore option (a) is correct.

#### 8. Question

Question is given followed by two Statements I and II. Consider the Question and the Statements.

Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.

Question: What is the difference of their ages?

Statement-I: The age of P is greater than the age of Q. Statement-II: The sum of their ages is 44/27 times their difference.

Which one of the following is correct in respect of the above Question and the Statements?

• (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

• (b) The Question can be answered by using either Statement alone

• (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

• (d) The Question cannot be answered even by using both the Statements together

Answer – A

Solution:

Given that,

Age of P and Q is less than 100 years but more than 10 years. Digits of P when interchanged the number represents Q.

Statement I: The age of P is greater than the age of Q. Statement II: The sum of their ages is 44/27 times their difference.

Let P = 10x + y and Q = 10y + x.

Statement I: 10x + y > 10y + x ⇒ x > y, but the difference cannot be determined. Hence statement I is insufficient.

Statement II: 11x + 11y = (44/27)(9x − 9y) 11(x + y) = (44/3)(x − y) Multiply by 3: 33x + 33y = 44x − 44y ⇒ 11x = 77y ⇒ x = 7y.

With 1 ≤ y ≤ 9 and x ≤ 9, the only possibility is y = 1, x = 7. So P = 71 and Q = 17. Difference = 71 − 17 = 54.

Hence statement II is sufficient to answer the question.

Therefore option (a) is correct.

Answer – A

Solution:

Given that,

Age of P and Q is less than 100 years but more than 10 years. Digits of P when interchanged the number represents Q.

Statement I: The age of P is greater than the age of Q. Statement II: The sum of their ages is 44/27 times their difference.

Let P = 10x + y and Q = 10y + x.

Statement I: 10x + y > 10y + x ⇒ x > y, but the difference cannot be determined. Hence statement I is insufficient.

Statement II: 11x + 11y = (44/27)(9x − 9y) 11(x + y) = (44/3)(x − y) Multiply by 3: 33x + 33y = 44x − 44y ⇒ 11x = 77y ⇒ x = 7y.

With 1 ≤ y ≤ 9 and x ≤ 9, the only possibility is y = 1, x = 7. So P = 71 and Q = 17. Difference = 71 − 17 = 54.

Hence statement II is sufficient to answer the question.

Therefore option (a) is correct.

• Question 9 of 10 9. Question X said to Y, “At the time of your birth I was four times as old as you are at present.” If the present age of X is 50 years, then consider the following statements: After 10 years, the age of X would be three times the age of Y. 5 years ago, the age of X was eight times the age of Y. Which of the above statements is/are correct? (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2 Correct Answer – A Solution: Given that, X said to Y, “At the time of your birth I was four times as old as you are at present.” The present age of X is 50 years. Now, Let the present age of Y be a years. At Y’s birth, age of X = 50 − a. Given 50 − a = 4a ⇒ 50 = 5a ⇒ a = 10 years. After 10 years: Y = 10 + 10 = 20 years; X = 50 + 10 = 60 years. 60 = 3 × 20, so statement 1 is correct. 5 years ago: Y = 10 − 5 = 5 years; X = 50 − 5 = 45 years. 45 = 9 × 5, not 8 × 5, so statement 2 is incorrect. Hence option (a) is correct. Incorrect Answer – A Solution: Given that, X said to Y, “At the time of your birth I was four times as old as you are at present.” The present age of X is 50 years. Now, Let the present age of Y be a years. At Y’s birth, age of X = 50 − a. Given 50 − a = 4a ⇒ 50 = 5a ⇒ a = 10 years. After 10 years: Y = 10 + 10 = 20 years; X = 50 + 10 = 60 years. 60 = 3 × 20, so statement 1 is correct. 5 years ago: Y = 10 − 5 = 5 years; X = 50 − 5 = 45 years. 45 = 9 × 5, not 8 × 5, so statement 2 is incorrect. Hence option (a) is correct.

#### 9. Question

X said to Y, “At the time of your birth I was four times as old as you are at present.” If the present age of X is 50 years, then consider the following statements:

• After 10 years, the age of X would be three times the age of Y.

• 5 years ago, the age of X was eight times the age of Y.

Which of the above statements is/are correct?

• (a) 1 only

• (b) 2 only

• (c) Both 1 and 2

• (d) Neither 1 nor 2

Answer – A Solution:

Given that,

X said to Y, “At the time of your birth I was four times as old as you are at present.” The present age of X is 50 years.

Let the present age of Y be a years. At Y’s birth, age of X = 50 − a. Given 50 − a = 4a ⇒ 50 = 5a ⇒ a = 10 years.

• After 10 years: Y = 10 + 10 = 20 years; X = 50 + 10 = 60 years. 60 = 3 × 20, so statement 1 is correct.

• 5 years ago: Y = 10 − 5 = 5 years; X = 50 − 5 = 45 years. 45 = 9 × 5, not 8 × 5, so statement 2 is incorrect.

Hence option (a) is correct.

Answer – A Solution:

Given that,

X said to Y, “At the time of your birth I was four times as old as you are at present.” The present age of X is 50 years.

Let the present age of Y be a years. At Y’s birth, age of X = 50 − a. Given 50 − a = 4a ⇒ 50 = 5a ⇒ a = 10 years.

• After 10 years: Y = 10 + 10 = 20 years; X = 50 + 10 = 60 years. 60 = 3 × 20, so statement 1 is correct.

• 5 years ago: Y = 10 − 5 = 5 years; X = 50 − 5 = 45 years. 45 = 9 × 5, not 8 × 5, so statement 2 is incorrect.

Hence option (a) is correct.

• Question 10 of 10 10. Question History, wrote E.H. Carr, is not simply a collection of facts but a dialogue between the past and the present. Every generation rewrites history, not because the events have changed, but because their questions and concerns have changed. The French Revolution, for instance, has been celebrated as the birth of liberty, condemned as a reign of terror, and studied as a struggle of class interests — each interpretation revealing more about the historian’s age than about 1789 itself. Critics argue that this makes history subjective, vulnerable to bias. Yet others insist that total objectivity is a myth, and that awareness of our standpoint can itself sharpen historical insight. The paradox lies in this: history seeks to tell us what really happened, yet it can only be told through the lens of those who ask the questions. In the context of the above passage, what is the central paradox that the passage highlights? (a) History claims to be objective, yet its interpretation is shaped by the historian’s context. (b) History deals with unchanging facts, yet these facts are often false. (c) History can be rewritten endlessly, yet it never reveals anything new. (d) History provides certainty about the past, yet leaves the present unexplained. Correct Solution: (a) Explanation: The paradox emphasized is that history aims at objectivity but inevitably reflects the historian’s standpoint. Option (b) is incorrect — facts are not said to be false. Option (c) misstates — reinterpretation does reveal insights. Option (d) is not supported. Hence, (a) is correct. Incorrect Solution: (a) Explanation: The paradox emphasized is that history aims at objectivity but inevitably reflects the historian’s standpoint. Option (b) is incorrect — facts are not said to be false. Option (c) misstates — reinterpretation does reveal insights. Option (d) is not supported. Hence, (a) is correct.

#### 10. Question

History, wrote E.H. Carr, is not simply a collection of facts but a dialogue between the past and the present. Every generation rewrites history, not because the events have changed, but because their questions and concerns have changed. The French Revolution, for instance, has been celebrated as the birth of liberty, condemned as a reign of terror, and studied as a struggle of class interests — each interpretation revealing more about the historian’s age than about 1789 itself. Critics argue that this makes history subjective, vulnerable to bias. Yet others insist that total objectivity is a myth, and that awareness of our standpoint can itself sharpen historical insight. The paradox lies in this: history seeks to tell us what really happened, yet it can only be told through the lens of those who ask the questions.

In the context of the above passage, what is the central paradox that the passage highlights?

• (a) History claims to be objective, yet its interpretation is shaped by the historian’s context.

• (b) History deals with unchanging facts, yet these facts are often false.

• (c) History can be rewritten endlessly, yet it never reveals anything new.

• (d) History provides certainty about the past, yet leaves the present unexplained.

Solution: (a)

Explanation: The paradox emphasized is that history aims at objectivity but inevitably reflects the historian’s standpoint. Option (b) is incorrect — facts are not said to be false. Option (c) misstates — reinterpretation does reveal insights. Option (d) is not supported. Hence, (a) is correct.

Solution: (a)

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