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)?
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. -
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?
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. 2,00,000From 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 = 720Incorrect
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. 2,00,000From 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 -
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?
Correct
Answer: B
Solution:
Incomes = 5I : 3I
Expenses = 4E : 2E
Savings = Rs. 2,000 eachSo, 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 eachSo, 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. -
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?
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. -
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?
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).
