UPSC Insta–DART (Daily Aptitude and Reasoning Test) 7 Nov 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 In a certain code, if 125 is written as 512 and 343 is written as 1000, then how is 27 written in that code? (a) 216 (b) 343 (c) 512 (d) 729 Correct Answer: (a) Explanation 125 = 5×5×5 is coded as 512 = 8×8×8 343 = 7×7×7 is coded as 1000 = 10×10×10 So, 27 = 3×3×3 would be coded as 216 = 6×6×6 Hence, option (a) is correct. Incorrect Answer: (a) Explanation 125 = 5×5×5 is coded as 512 = 8×8×8 343 = 7×7×7 is coded as 1000 = 10×10×10 So, 27 = 3×3×3 would be coded as 216 = 6×6×6 Hence, option (a) is correct.

#### 1. Question

In a certain code, if 125 is written as 512 and 343 is written as 1000, then how is 27 written in that code?

Answer: (a)

Explanation 125 = 5×5×5 is coded as 512 = 8×8×8 343 = 7×7×7 is coded as 1000 = 10×10×10 So, 27 = 3×3×3 would be coded as 216 = 6×6×6

Hence, option (a) is correct.

Answer: (a)

Explanation 125 = 5×5×5 is coded as 512 = 8×8×8 343 = 7×7×7 is coded as 1000 = 10×10×10 So, 27 = 3×3×3 would be coded as 216 = 6×6×6

Hence, option (a) is correct.

• Question 2 of 5 2. Question A question is given followed by two statements: Question: What is the speed of the train? Statements: I. The train crosses a platform 300 m long in 30 seconds. II. The train crosses a man standing on the platform in 18 seconds. (a) If statement I alone is sufficient to answer the question. (b) If statement II alone is sufficient to answer the question. (c) If both the statements I & II together are not sufficient to answer the question. (d) If both the statements I & II together are sufficient to answer the question. Correct Answer: (d) Explanation: Let the train’s length = L metres and its speed = S m/s. From Statement I: Total distance = L + 300; time = 30 s ⇒ S = (L + 300)/30. (Two variables ⇒ not sufficient.) From Statement II: Distance = L; time = 18 s ⇒ S = L/18. Solving both equations simultaneously: L/18 = (L + 300)/30 ⇒ 30L = 18L + 5400 ⇒ 12L = 5400 ⇒ L = 450 m. Then S = 450 / 18 = 25 m/s = 25 × 18/5 = 90 km/h. Both statements together are required. Incorrect Answer: (d) Explanation: Let the train’s length = L metres and its speed = S m/s. From Statement I: Total distance = L + 300; time = 30 s ⇒ S = (L + 300)/30. (Two variables ⇒ not sufficient.) From Statement II: Distance = L; time = 18 s ⇒ S = L/18. Solving both equations simultaneously: L/18 = (L + 300)/30 ⇒ 30L = 18L + 5400 ⇒ 12L = 5400 ⇒ L = 450 m. Then S = 450 / 18 = 25 m/s = 25 × 18/5 = 90 km/h. Both statements together are required.

#### 2. Question

A question is given followed by two statements:

Question: What is the speed of the train? Statements: I. The train crosses a platform 300 m long in 30 seconds. II. The train crosses a man standing on the platform in 18 seconds.

• (a) If statement I alone is sufficient to answer the question.

• (b) If statement II alone is sufficient to answer the question.

• (c) If both the statements I & II together are not sufficient to answer the question.

• (d) If both the statements I & II together are sufficient to answer the question.

Answer: (d)

Explanation: Let the train’s length = L metres and its speed = S m/s.

From Statement I: Total distance = L + 300; time = 30 s ⇒ S = (L + 300)/30. (Two variables ⇒ not sufficient.)

From Statement II: Distance = L; time = 18 s ⇒ S = L/18.

Solving both equations simultaneously: L/18 = (L + 300)/30 ⇒ 30L = 18L + 5400 ⇒ 12L = 5400 ⇒ L = 450 m. Then S = 450 / 18 = 25 m/s = 25 × 18/5 = 90 km/h.

Both statements together are required.

Answer: (d)

Explanation: Let the train’s length = L metres and its speed = S m/s.

From Statement I: Total distance = L + 300; time = 30 s ⇒ S = (L + 300)/30. (Two variables ⇒ not sufficient.)

From Statement II: Distance = L; time = 18 s ⇒ S = L/18.

Solving both equations simultaneously: L/18 = (L + 300)/30 ⇒ 30L = 18L + 5400 ⇒ 12L = 5400 ⇒ L = 450 m. Then S = 450 / 18 = 25 m/s = 25 × 18/5 = 90 km/h.

Both statements together are required.

• Question 3 of 5 3. Question A fund of ₹75,600 is to be shared among 8 lecturers, 24 staff, and 48 students in the per-head ratio 5 : 4 : 3. Before distributing, 10% of the total is kept aside for a welfare fund and then deducted proportionately from each group’s allocation. What is the final per-student share? (a) ₹702 (b) ₹720 (c) ₹729 (d) ₹750 Correct Answer: (c) Solution: Group-weighted parts: Lecturers: 8×5 = 40 Staff: 24×4 = 96 Students: 48×3 = 144 Total parts = 40 + 96 + 144 = 280. Each part (before deduction) = 75,600 / 280 = ₹270. Initial allocations: • Lecturers = 40×270 = ₹10,800 • Staff = 96×270 = ₹25,920 • Students = 144×270 = ₹38,880 Per student (initial) = 38,880 / 48 = ₹810. 10% kept aside proportionately ⇒ everyone loses 10%. Final per-student = 810 × 0.90 = ₹729. Incorrect Answer: (c) Solution: Group-weighted parts: Lecturers: 8×5 = 40 Staff: 24×4 = 96 Students: 48×3 = 144 Total parts = 40 + 96 + 144 = 280. Each part (before deduction) = 75,600 / 280 = ₹270. Initial allocations: • Lecturers = 40×270 = ₹10,800 • Staff = 96×270 = ₹25,920 • Students = 144×270 = ₹38,880 Per student (initial) = 38,880 / 48 = ₹810. 10% kept aside proportionately ⇒ everyone loses 10%. Final per-student = 810 × 0.90 = ₹729.

#### 3. Question

A fund of ₹75,600 is to be shared among 8 lecturers, 24 staff, and 48 students in the per-head ratio 5 : 4 : 3. Before distributing, 10% of the total is kept aside for a welfare fund and then deducted proportionately from each group’s allocation. What is the final per-student share?

Answer: (c)

Solution: Group-weighted parts: Lecturers: 8×5 = 40 Staff: 24×4 = 96 Students: 48×3 = 144 Total parts = 40 + 96 + 144 = 280.

Each part (before deduction) = 75,600 / 280 = ₹270. Initial allocations: • Lecturers = 40×270 = ₹10,800 • Staff = 96×270 = ₹25,920 • Students = 144×270 = ₹38,880 Per student (initial) = 38,880 / 48 = ₹810.

10% kept aside proportionately ⇒ everyone loses 10%. Final per-student = 810 × 0.90 = ₹729.

Answer: (c)

Solution: Group-weighted parts: Lecturers: 8×5 = 40 Staff: 24×4 = 96 Students: 48×3 = 144 Total parts = 40 + 96 + 144 = 280.

10% kept aside proportionately ⇒ everyone loses 10%. Final per-student = 810 × 0.90 = ₹729.

• Question 4 of 5 4. Question A, B and C invest respectively ₹9,000 for 12 months, ₹12,000 for 9 months, and ₹15,000 for 6 months. C is the working partner and takes 8% of the profit as commission. If the total profit is ₹17,000, what is C’s share (including commission)? (a) ₹5,520 (b) ₹5,760 (c) ₹5,960 (d) ₹6,160 Correct Answer: (c) Solution: Capital–months: A = 9,000×12 = 108,000; B = 12,000×9 = 108,000; C = 15,000×6 = 90,000 Ratio A : B : C = 108,000 : 108,000 : 90,000 = 6 : 6 : 5 (sum = 17) Commission to C = 8% of 17,000 = ₹1,360 Balance for division = 17,000 − 1,360 = ₹15,640 From balance, C’s part = (5/17)×15,640 = 5×920 = ₹4,600 Total C (with commission) = 4,600 + 1,360 = ₹5,960. Incorrect Answer: (c) Solution: Capital–months: A = 9,000×12 = 108,000; B = 12,000×9 = 108,000; C = 15,000×6 = 90,000 Ratio A : B : C = 108,000 : 108,000 : 90,000 = 6 : 6 : 5 (sum = 17) Commission to C = 8% of 17,000 = ₹1,360 Balance for division = 17,000 − 1,360 = ₹15,640 From balance, C’s part = (5/17)×15,640 = 5×920 = ₹4,600 Total C (with commission) = 4,600 + 1,360 = ₹5,960.

#### 4. Question

A, B and C invest respectively ₹9,000 for 12 months, ₹12,000 for 9 months, and ₹15,000 for 6 months. C is the working partner and takes 8% of the profit as commission. If the total profit is ₹17,000, what is C’s share (including commission)?

• (a) ₹5,520

• (b) ₹5,760

• (c) ₹5,960

• (d) ₹6,160

Answer: (c)

Solution: Capital–months: A = 9,000×12 = 108,000; B = 12,000×9 = 108,000; C = 15,000×6 = 90,000 Ratio A : B : C = 108,000 : 108,000 : 90,000 = 6 : 6 : 5 (sum = 17)

Commission to C = 8% of 17,000 = ₹1,360 Balance for division = 17,000 − 1,360 = ₹15,640

From balance, C’s part = (5/17)×15,640 = 5×920 = ₹4,600 Total C (with commission) = 4,600 + 1,360 = ₹5,960.

Answer: (c)

Solution: Capital–months: A = 9,000×12 = 108,000; B = 12,000×9 = 108,000; C = 15,000×6 = 90,000 Ratio A : B : C = 108,000 : 108,000 : 90,000 = 6 : 6 : 5 (sum = 17)

Commission to C = 8% of 17,000 = ₹1,360 Balance for division = 17,000 − 1,360 = ₹15,640

From balance, C’s part = (5/17)×15,640 = 5×920 = ₹4,600 Total C (with commission) = 4,600 + 1,360 = ₹5,960.

• Question 5 of 5 5. Question At the end of one year, what is the ratio of profits of A and B (after paying A a fixed remuneration from profits before division)? I. A invested ₹60,000 for 12 months; B invested ₹90,000 for 8 months. II. A, as the working partner, is to receive a fixed remuneration of ₹24,000 from the year’s profit before division. III. The total profit for the year was ₹1,44,000. Which of the following is correct with respect to above? (a) I and II only (b) II and III only (b) II and III only (d) Even with all I, II and III together, the answer cannot be arrived at. Correct Answer: (c) Explanation: From I: capital–months → A = 60,000 × 12 = 7,20,000; B = 90,000 × 8 = 7,20,000 → balance ratio 1 : 1. From II and III: Total profit = ₹1,44,000; pay fixed ₹24,000 to A; balance = ₹1,20,000 to be split equally → ₹60,000 each. Thus final: A = 24,000 + 60,000 = ₹84,000; B = ₹60,000 → ratio 84 : 60 = 7 : 5. Here the fixed remuneration makes the ratio depend on the actual total profit, so III is essential; all I, II and III together are required. Incorrect Answer: (c) Explanation: From I: capital–months → A = 60,000 × 12 = 7,20,000; B = 90,000 × 8 = 7,20,000 → balance ratio 1 : 1. From II and III: Total profit = ₹1,44,000; pay fixed ₹24,000 to A; balance = ₹1,20,000 to be split equally → ₹60,000 each. Thus final: A = 24,000 + 60,000 = ₹84,000; B = ₹60,000 → ratio 84 : 60 = 7 : 5. Here the fixed remuneration makes the ratio depend on the actual total profit, so III is essential; all I, II and III together are required.

#### 5. Question

At the end of one year, what is the ratio of profits of A and B (after paying A a fixed remuneration from profits before division)?

I. A invested ₹60,000 for 12 months; B invested ₹90,000 for 8 months. II. A, as the working partner, is to receive a fixed remuneration of ₹24,000 from the year’s profit before division. III. The total profit for the year was ₹1,44,000.

Which of the following is correct with respect to above?

• (a) I and II only

• (b) II and III only

• (d) Even with all I, II and III together, the answer cannot be arrived at.

Answer: (c)

Explanation: From I: capital–months → A = 60,000 × 12 = 7,20,000; B = 90,000 × 8 = 7,20,000 → balance ratio 1 : 1. From II and III: Total profit = ₹1,44,000; pay fixed ₹24,000 to A; balance = ₹1,20,000 to be split equally → ₹60,000 each. Thus final: A = 24,000 + 60,000 = ₹84,000; B = ₹60,000 → ratio 84 : 60 = 7 : 5. Here the fixed remuneration makes the ratio depend on the actual total profit, so III is essential; all I, II and III together are required.

Answer: (c)

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