UPSC Insta–DART (Daily Aptitude and Reasoning Test) 13 Aug 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 5 1. Question A is married to B. C is the daughter of A. D is the husband of C. E is the father of D. F is the brother of C. G is the wife of F. Then, consider the following- I. B is the mother of C II. A is the father-in-law of D III. E is the father-in-law of C IV. F is the son of A V. G is A’s daughter-in-law VI. E is the grandfather of A’s grandchildren How many of the above statements are definitely true? (a) Only three (b) Only four (c) Only five (d) All six Correct Answer: D Explanation: A and B are married C is daughter of A → C is child of both A and B D is husband of C E is father of D F is brother of C → Son of A and B G is wife of F Now evaluate: B is the mother of C → A married to B, C is their daughter → True II. A is father-in-law of D → D is C’s husband → A is C’s father → True III. E is father-in-law of C → D is C’s husband, E is D’s father → True IV. F is son of A → F is brother of C, and C is daughter of A → True V. G is A’s daughter-in-law → G is F’s wife, F is A’s son → True VI. E is grandfather of A’s grandchildren → C (daughter) and F (son) are A’s kids → C is married to D → Their children = A’s grandchildren → E is father of D → E is grandfather of C’s kids → True Hence, All six statements are true Incorrect Answer: D Explanation: A and B are married C is daughter of A → C is child of both A and B D is husband of C E is father of D F is brother of C → Son of A and B G is wife of F Now evaluate: B is the mother of C → A married to B, C is their daughter → True II. A is father-in-law of D → D is C’s husband → A is C’s father → True III. E is father-in-law of C → D is C’s husband, E is D’s father → True IV. F is son of A → F is brother of C, and C is daughter of A → True V. G is A’s daughter-in-law → G is F’s wife, F is A’s son → True VI. E is grandfather of A’s grandchildren → C (daughter) and F (son) are A’s kids → C is married to D → Their children = A’s grandchildren → E is father of D → E is grandfather of C’s kids → True Hence, All six statements are true

#### 1. Question

A is married to B. C is the daughter of A. D is the husband of C. E is the father of D. F is the brother of C. G is the wife of F. Then, consider the following-

I. B is the mother of C II. A is the father-in-law of D III. E is the father-in-law of C IV. F is the son of A V. G is A’s daughter-in-law VI. E is the grandfather of A’s grandchildren

How many of the above statements are definitely true?

• (a) Only three

• (b) Only four

• (c) Only five

• (d) All six

Explanation:

• A and B are married

• C is daughter of A → C is child of both A and B

• D is husband of C

• E is father of D

• F is brother of C → Son of A and B

• G is wife of F

Now evaluate:

• B is the mother of C → A married to B, C is their daughter → True II. A is father-in-law of D → D is C’s husband → A is C’s father → True III. E is father-in-law of C → D is C’s husband, E is D’s father → True IV. F is son of A → F is brother of C, and C is daughter of A → True V. G is A’s daughter-in-law → G is F’s wife, F is A’s son → True VI. E is grandfather of A’s grandchildren → C (daughter) and F (son) are A’s kids → C is married to D → Their children = A’s grandchildren → E is father of D → E is grandfather of C’s kids → True

Hence, All six statements are true

Explanation:

• A and B are married

• C is daughter of A → C is child of both A and B

• D is husband of C

• E is father of D

• F is brother of C → Son of A and B

• G is wife of F

Now evaluate:

Hence, All six statements are true

• Question 2 of 5 2. Question The ratio of the monthly income of Asha and Rekha is 3 : 4. Question: What is the ratio of their monthly savings? Statement I: Rekha spends 75% of her income. Statement II: The difference in monthly savings between Rekha and Asha is ₹6,000. Statement III: The expenditures of Asha and Rekha are in the ratio 9 : 15. Which of the following is correct with respect to above? (a) Statements I and II together are sufficient (b) Statements II and III together are sufficient (c) Statements I and III together are sufficient (d) All three statements together are required Correct Answer: C Explanation: Let incomes: Asha = 3x, Rekha = 4x From Statement I: Rekha spends 75% → spends = 0.75 × 4x = 3x Savings = 4x − 3x = x From Statement III: Expenditure ratio Asha : Rekha = 9 : 15 = 3x : 5x Rekha’s expenditure = 3x (from above) So, Asha’s expenditure = (9/15) × 3x = 1.8x Asha’s income = 3x ⇒ savings = 3x − 1.8x = 1.2x Now: Savings ratio Asha : Rekha = 1.2x : x = 12 : 10 = 6 : 5 Statements I and III together are sufficient Correct answer: (c) Incorrect Answer: C Explanation: Let incomes: Asha = 3x, Rekha = 4x From Statement I: Rekha spends 75% → spends = 0.75 × 4x = 3x Savings = 4x − 3x = x From Statement III: Expenditure ratio Asha : Rekha = 9 : 15 = 3x : 5x Rekha’s expenditure = 3x (from above) So, Asha’s expenditure = (9/15) × 3x = 1.8x Asha’s income = 3x ⇒ savings = 3x − 1.8x = 1.2x Now: Savings ratio Asha : Rekha = 1.2x : x = 12 : 10 = 6 : 5 Statements I and III together are sufficient Correct answer: (c)

#### 2. Question

The ratio of the monthly income of Asha and Rekha is 3 : 4. Question: What is the ratio of their monthly savings?

Statement I: Rekha spends 75% of her income. Statement II: The difference in monthly savings between Rekha and Asha is ₹6,000. Statement III: The expenditures of Asha and Rekha are in the ratio 9 : 15.

Which of the following is correct with respect to above?

• (a) Statements I and II together are sufficient

• (b) Statements II and III together are sufficient

• (c) Statements I and III together are sufficient

• (d) All three statements together are required

Explanation: Let incomes: Asha = 3x, Rekha = 4x

From Statement I: Rekha spends 75% → spends = 0.75 × 4x = 3x Savings = 4x − 3x = x

From Statement III: Expenditure ratio Asha : Rekha = 9 : 15 = 3x : 5x Rekha’s expenditure = 3x (from above) So, Asha’s expenditure = (9/15) × 3x = 1.8x Asha’s income = 3x ⇒ savings = 3x − 1.8x = 1.2x

Now: Savings ratio Asha : Rekha = 1.2x : x = 12 : 10 = 6 : 5

Statements I and III together are sufficient Correct answer: (c)

Explanation: Let incomes: Asha = 3x, Rekha = 4x

From Statement I: Rekha spends 75% → spends = 0.75 × 4x = 3x Savings = 4x − 3x = x

Now: Savings ratio Asha : Rekha = 1.2x : x = 12 : 10 = 6 : 5

Statements I and III together are sufficient Correct answer: (c)

• Question 3 of 5 3. Question A cylindrical drum has base diameter of 7 m and a height of 18 m. It is filled with water to a height of 3 m. If N identical marbles of diameter 1.4 m each are dropped into the drum, then the height of the water in the drum would rise upto 11.4 m. What is the value of N? (a) 325 (b) 225 (c) 275 (d) 295 Correct Answer: B Radius of drum = 7/2 = 3.5 m Radius of each marble = 1.4/2 = 0.7 m Rise in water level = 11.4 – 3 = 8.4 m Volume of the water displaced by N marbles = (base area) × (rise in water level) ∴ N {(4π (0.7)3)/3} = π (3.5)2 × 8.4 Or N = [(3.5)2 × 8.4 × 3] / [4 × (0.7)3] Or N = 225 Hence, option (b) is the right answer. Incorrect Answer: B Radius of drum = 7/2 = 3.5 m Radius of each marble = 1.4/2 = 0.7 m Rise in water level = 11.4 – 3 = 8.4 m Volume of the water displaced by N marbles = (base area) × (rise in water level) ∴ N {(4π (0.7)3)/3} = π (3.5)2 × 8.4 Or N = [(3.5)2 × 8.4 × 3] / [4 × (0.7)3] Or N = 225 Hence, option (b) is the right answer.

#### 3. Question

A cylindrical drum has base diameter of 7 m and a height of 18 m. It is filled with water to a height of 3 m. If N identical marbles of diameter 1.4 m each are dropped into the drum, then the height of the water in the drum would rise upto 11.4 m. What is the value of N?

Radius of drum = 7/2 = 3.5 m Radius of each marble = 1.4/2 = 0.7 m

Rise in water level = 11.4 – 3 = 8.4 m

Volume of the water displaced by N marbles = (base area) × (rise in water level)

∴ N {(4π (0.7)3)/3} = π (3.5)2 × 8.4

Or N = [(3.5)2 × 8.4 × 3] / [4 × (0.7)3]

Or N = 225

Hence, option (b) is the right answer.

Radius of drum = 7/2 = 3.5 m Radius of each marble = 1.4/2 = 0.7 m

Rise in water level = 11.4 – 3 = 8.4 m

Volume of the water displaced by N marbles = (base area) × (rise in water level)

∴ N {(4π (0.7)3)/3} = π (3.5)2 × 8.4

Or N = [(3.5)2 × 8.4 × 3] / [4 × (0.7)3]

Or N = 225

Hence, option (b) is the right answer.

• Question 4 of 5 4. Question A person saves Rs. 5 on Day 1, Rs. 10 on Day 2, Rs. 15 on Day 3, and so on. On which day will his total savings first exceed Rs. 500 and also be a multiple of 25? (a) 12th day (b) 13th day (c) 14th day (d) 15th day Correct Answer: C Solution Daily savings = 5, 10, 15, 20, … (AP with a = 5, d = 5) Sum of n terms = We want the smallest n such that sum > 500 and divisible by 25 Try n = 12 → S = 5×12×13 / 2 = 390 → not > 500 n = 13 → 5×13×14 / 2 = 455 n = 14 → 5×14×15 / 2 = 525 and divisible by 25 Hence, option c is correct. Incorrect Answer: C Solution Daily savings = 5, 10, 15, 20, … (AP with a = 5, d = 5) Sum of n terms = We want the smallest n such that sum > 500 and divisible by 25 Try n = 12 → S = 5×12×13 / 2 = 390 → not > 500 n = 13 → 5×13×14 / 2 = 455 n = 14 → 5×14×15 / 2 = 525 and divisible by 25 Hence, option c is correct.

#### 4. Question

A person saves Rs. 5 on Day 1, Rs. 10 on Day 2, Rs. 15 on Day 3, and so on. On which day will his total savings first exceed Rs. 500 and also be a multiple of 25?

• (a) 12th day

• (b) 13th day

• (c) 14th day

• (d) 15th day

Answer: C

Solution

Daily savings = 5, 10, 15, 20, … (AP with a = 5, d = 5) Sum of n terms =

We want the smallest n such that sum > 500 and divisible by 25

Try n = 12 → S = 5×12×13 / 2 = 390 → not > 500 n = 13 → 5×13×14 / 2 = 455 n = 14 → 5×14×15 / 2 = 525 and divisible by 25

Hence, option c is correct.

Answer: C

Solution

Daily savings = 5, 10, 15, 20, … (AP with a = 5, d = 5) Sum of n terms =

We want the smallest n such that sum > 500 and divisible by 25

Try n = 12 → S = 5×12×13 / 2 = 390 → not > 500 n = 13 → 5×13×14 / 2 = 455 n = 14 → 5×14×15 / 2 = 525 and divisible by 25

Hence, option c is correct.

• Question 5 of 5 5. Question What is the number of times the digit ‘1’ is used in numbering a 120-page book? (a) 64 (b) 53 (c) 55 (d) 67 Correct Answer: B Solution: Units place (ends in 1): 1, 11, …, 111 Last such number ≤ 120 is 111 Total = [(111−1)/10] + 1 = 12 Tens place: 10–19 → 10 numbers 110–119 → 10 numbers → Total = 20 Hundreds place: 100–120 → all have 1 as hundreds → 21 numbers Total = 12 + 20 + 21 = 53 Incorrect Answer: B Solution: Units place (ends in 1): 1, 11, …, 111 Last such number ≤ 120 is 111 Total = [(111−1)/10] + 1 = 12 Tens place: 10–19 → 10 numbers 110–119 → 10 numbers → Total = 20 Hundreds place: 100–120 → all have 1 as hundreds → 21 numbers Total = 12 + 20 + 21 = 53

#### 5. Question

What is the number of times the digit ‘1’ is used in numbering a 120-page book?

Solution: Units place (ends in 1): 1, 11, …, 111

• Last such number ≤ 120 is 111

• Total = [(111−1)/10] + 1 = 12

Tens place:

• 10–19 → 10 numbers

• 110–119 → 10 numbers → Total = 20

Hundreds place:

• 100–120 → all have 1 as hundreds → 21 numbers

Total = 12 + 20 + 21 = 53