UPSC Insta–DART (Daily Aptitude and Reasoning Test) 18 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 5 1. Question Ten persons V, W, X, Y, Z and five others speak in random order. What is the chance that V speaks after W, W after X, X after Y, and Y after Z (i.e., V after W after X after Y after Z)? (a) 1/60 (b) 1/120 (c) 1/24 (d) 1/6 Correct Answer: (b) Solution: Total number of ways = 10! Number of ways to place V, W, X, Y, Z in the given order = ¹⁰C₅ Arrangements of the remaining 5 persons = 5! Favourable ways = ¹⁰C₅ × 5! Required chance = (¹⁰C₅ × 5!) / 10! = 1/5! = 1/120 Hence, option (b) is correct. Incorrect Answer: (b) Solution: Total number of ways = 10! Number of ways to place V, W, X, Y, Z in the given order = ¹⁰C₅ Arrangements of the remaining 5 persons = 5! Favourable ways = ¹⁰C₅ × 5! Required chance = (¹⁰C₅ × 5!) / 10! = 1/5! = 1/120 Hence, option (b) is correct.

#### 1. Question

Ten persons V, W, X, Y, Z and five others speak in random order. What is the chance that V speaks after W, W after X, X after Y, and Y after Z (i.e., V after W after X after Y after Z)?

Answer: (b) Solution: Total number of ways = 10! Number of ways to place V, W, X, Y, Z in the given order = ¹⁰C₅ Arrangements of the remaining 5 persons = 5! Favourable ways = ¹⁰C₅ × 5! Required chance = (¹⁰C₅ × 5!) / 10! = 1/5! = 1/120 Hence, option (b) is correct.

• Question 2 of 5 2. Question In a town, 12% of families earn less than Rs. 40,000 per year, 10% of families earn more than Rs. 3,00,000 per year, 28% of families earn more than Rs. 2,00,000 per year and 2400 families earn between Rs. 40,000 and Rs. 2,00,000 per year. How many families earn between Rs. 2,00,000 and Rs. 3,00,000 per year? (a) 600 (b) 720 (c) 840 (d) 1160 Correct Answer: B Solution: 12% earn below Rs. 40,000 10% earn above Rs. 3,00,000 28% earn above Rs. 2,00,000 2400 families are between Rs. 40,000 and Rs. 2,00,000 From Rs. 2,00,000 to Rs. 3,00,000 = 28% − 10% = 18% Families between Rs. 40,000 and Rs. 2,00,000 = 100 − (12 + 18 + 10) = 60% Total families = 2400 × (100/60) = 4000 Families between Rs. 2,00,000 and Rs. 3,00,000 = 18% of 4000 = 720 Incorrect Answer: B Solution: 12% earn below Rs. 40,000 10% earn above Rs. 3,00,000 28% earn above Rs. 2,00,000 2400 families are between Rs. 40,000 and Rs. 2,00,000 From Rs. 2,00,000 to Rs. 3,00,000 = 28% − 10% = 18% Families between Rs. 40,000 and Rs. 2,00,000 = 100 − (12 + 18 + 10) = 60% Total families = 2400 × (100/60) = 4000 Families between Rs. 2,00,000 and Rs. 3,00,000 = 18% of 4000 = 720

#### 2. Question

In a town, 12% of families earn less than Rs. 40,000 per year, 10% of families earn more than Rs. 3,00,000 per year, 28% of families earn more than Rs. 2,00,000 per year and 2400 families earn between Rs. 40,000 and Rs. 2,00,000 per year. How many families earn between Rs. 2,00,000 and Rs. 3,00,000 per year?

Solution: 12% earn below Rs. 40,000 10% earn above Rs. 3,00,000 28% earn above Rs. 2,00,000 2400 families are between Rs. 40,000 and Rs. 2,00,000

From Rs. 2,00,000 to Rs. 3,00,000 = 28% − 10% = 18% Families between Rs. 40,000 and Rs. 2,00,000 = 100 − (12 + 18 + 10) = 60% Total families = 2400 × (100/60) = 4000 Families between Rs. 2,00,000 and Rs. 3,00,000 = 18% of 4000 = 720

Solution: 12% earn below Rs. 40,000 10% earn above Rs. 3,00,000 28% earn above Rs. 2,00,000 2400 families are between Rs. 40,000 and Rs. 2,00,000

• Question 3 of 5 3. Question The monthly incomes of A and B are in the ratio 5:3 and their monthly expenses are in the ratio 4:2. Each saves Rs. 2,000 per month. What is their total monthly income? (a) Rs. 14,000 (b) Rs. 16,000 (c) Rs. 18,000 (d) Rs. 20,000 Correct Answer: B Solution: Incomes = 5I : 3I Expenses = 4E : 2E Savings = Rs. 2,000 each So, 5I − 4E = 2000 … (i) 3I − 2E = 2000 … (ii) Multiply (ii) by 2: 6I − 4E = 4000 Subtract (i): (6I − 4E) − (5I − 4E) = 4000 − 2000 I = 2000 From (ii): 3(2000) − 2E = 2000 ⇒ 6000 − 2E = 2000 ⇒ 2E = 4000 ⇒ E = 2000 Income of A = 5 × 2000 = 10,000 Income of B = 3 × 2000 = 6,000 Total = 16,000 Hence, option (b) is correct. Incorrect Answer: B Solution: Incomes = 5I : 3I Expenses = 4E : 2E Savings = Rs. 2,000 each So, 5I − 4E = 2000 … (i) 3I − 2E = 2000 … (ii) Multiply (ii) by 2: 6I − 4E = 4000 Subtract (i): (6I − 4E) − (5I − 4E) = 4000 − 2000 I = 2000 From (ii): 3(2000) − 2E = 2000 ⇒ 6000 − 2E = 2000 ⇒ 2E = 4000 ⇒ E = 2000 Income of A = 5 × 2000 = 10,000 Income of B = 3 × 2000 = 6,000 Total = 16,000 Hence, option (b) is correct.

#### 3. Question

The monthly incomes of A and B are in the ratio 5:3 and their monthly expenses are in the ratio 4:2. Each saves Rs. 2,000 per month. What is their total monthly income?

• (a) Rs. 14,000

• (b) Rs. 16,000

• (c) Rs. 18,000

• (d) Rs. 20,000

Solution: Incomes = 5I : 3I Expenses = 4E : 2E Savings = Rs. 2,000 each

So, 5I − 4E = 2000 … (i) 3I − 2E = 2000 … (ii)

Multiply (ii) by 2: 6I − 4E = 4000 Subtract (i): (6I − 4E) − (5I − 4E) = 4000 − 2000 I = 2000 From (ii): 3(2000) − 2E = 2000 ⇒ 6000 − 2E = 2000 ⇒ 2E = 4000 ⇒ E = 2000 Income of A = 5 × 2000 = 10,000 Income of B = 3 × 2000 = 6,000 Total = 16,000 Hence, option (b) is correct.

Solution: Incomes = 5I : 3I Expenses = 4E : 2E Savings = Rs. 2,000 each

So, 5I − 4E = 2000 … (i) 3I − 2E = 2000 … (ii)

• Question 4 of 5 4. Question Two friends hire a cab. The total fare for both is such that 50% of it equals ₹25. Friend A has ₹30, which he realizes is 120% of his required share. His friend B contributes ₹20. What will be the balance left after paying the fare? (a) ₹20 (b) ₹15 (c) ₹10 (d) Nil Correct Answer: D Solution: Let total cost for two = T. Given 50% of T = 25 ⇒ T = (25 × 100)/50 = ₹50. Total money with A and B = 30 + 20 = ₹50. Balance left = 50 – 50 = Nil. Hence, option (d) is correct. Incorrect Answer: D Solution: Let total cost for two = T. Given 50% of T = 25 ⇒ T = (25 × 100)/50 = ₹50. Total money with A and B = 30 + 20 = ₹50. Balance left = 50 – 50 = Nil. Hence, option (d) is correct.

#### 4. Question

Two friends hire a cab. The total fare for both is such that 50% of it equals ₹25. Friend A has ₹30, which he realizes is 120% of his required share. His friend B contributes ₹20. What will be the balance left after paying the fare?

Solution: Let total cost for two = T. Given 50% of T = 25 ⇒ T = (25 × 100)/50 = ₹50. Total money with A and B = 30 + 20 = ₹50. Balance left = 50 – 50 = Nil. Hence, option (d) is correct.

• Question 5 of 5 5. Question X and Y invest in the ratio 2:5. After 8 months, X halves his capital while Y doubles his capital for the last 4 months. If the total profit at the end of the year is ₹45,000, what is Y’s share? (a) ₹30,000 (b) ₹32,000 (c) ₹36,000 (d) ₹38,000 Correct Answer: (c) Solution: Let initial capitals be X = 2k, Y = 5k. First 8 months: • X = 2k × 8 = 16k • Y = 5k × 8 = 40k Last 4 months: (X → k; Y → 10k) • X = 1k × 4 = 4k • Y = 10k × 4 = 40k Totals: • X = 16k + 4k = 20k • Y = 40k + 40k = 80k Ratio = 20 : 80 = 1 : 4 Total parts = 5 Y’s share = (4/5) × 45,000 = ₹36,000. Hence, option (c). Incorrect Answer: (c) Solution: Let initial capitals be X = 2k, Y = 5k. First 8 months: • X = 2k × 8 = 16k • Y = 5k × 8 = 40k Last 4 months: (X → k; Y → 10k) • X = 1k × 4 = 4k • Y = 10k × 4 = 40k Totals: • X = 16k + 4k = 20k • Y = 40k + 40k = 80k Ratio = 20 : 80 = 1 : 4 Total parts = 5 Y’s share = (4/5) × 45,000 = ₹36,000. Hence, option (c).

#### 5. Question

X and Y invest in the ratio 2:5. After 8 months, X halves his capital while Y doubles his capital for the last 4 months. If the total profit at the end of the year is ₹45,000, what is Y’s share?

• (a) ₹30,000

• (b) ₹32,000

• (c) ₹36,000

• (d) ₹38,000

Answer: (c) Solution: Let initial capitals be X = 2k, Y = 5k. First 8 months: • X = 2k × 8 = 16k • Y = 5k × 8 = 40k Last 4 months: (X → k; Y → 10k) • X = 1k × 4 = 4k • Y = 10k × 4 = 40k Totals: • X = 16k + 4k = 20k • Y = 40k + 40k = 80k Ratio = 20 : 80 = 1 : 4 Total parts = 5 Y’s share = (4/5) × 45,000 = ₹36,000. Hence, option (c).

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