UPSC Insta–DART (Daily Aptitude and Reasoning Test) 6 Jan 2026
Kartavya Desk Staff
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 From 1 January 2021, the price of bus diesel on the m-th day is 40 + 0.2m for all m. The price of train diesel is 55 + 0.15n for n = 1 to 120, and stays constant after day 120. On which date in 2021 do the two prices become equal? (a) 10 June (b) 12 June (c) 14 June (d) 16 June Correct Solution: First check before day 120: 40 + 0.2m = 55 + 0.15m −15 = −0.05m → m = 300 (not valid because >120). So use constant price after day 120. Train diesel becomes constant at: 55 + 0.15×120 = 55 + 18 = 73. Now set bus diesel = 73: 40 + 0.2m = 73 0.2m = 33 m = 165. Day 165 of 2021: Jan (31) → 31 Feb (28) → 59 Mar (31) → 90 Apr (30) → 120 May (31) → 151 Day 165 is 14 days into June → 14 June. Incorrect Solution: First check before day 120: 40 + 0.2m = 55 + 0.15m −15 = −0.05m → m = 300 (not valid because >120). So use constant price after day 120. Train diesel becomes constant at: 55 + 0.15×120 = 55 + 18 = 73. Now set bus diesel = 73: 40 + 0.2m = 73 0.2m = 33 m = 165. Day 165 of 2021: Jan (31) → 31 Feb (28) → 59 Mar (31) → 90 Apr (30) → 120 May (31) → 151 Day 165 is 14 days into June → 14 June.
#### 1. Question
From 1 January 2021, the price of bus diesel on the m-th day is 40 + 0.2m for all m. The price of train diesel is 55 + 0.15n for n = 1 to 120, and stays constant after day 120. On which date in 2021 do the two prices become equal?
• (a) 10 June
• (b) 12 June
• (c) 14 June
• (d) 16 June
Solution: First check before day 120: 40 + 0.2m = 55 + 0.15m −15 = −0.05m → m = 300 (not valid because >120).
So use constant price after day 120. Train diesel becomes constant at: 55 + 0.15×120 = 55 + 18 = 73.
Now set bus diesel = 73: 40 + 0.2m = 73 0.2m = 33 m = 165.
Day 165 of 2021: Jan (31) → 31 Feb (28) → 59 Mar (31) → 90 Apr (30) → 120 May (31) → 151 Day 165 is 14 days into June → 14 June.
Solution: First check before day 120: 40 + 0.2m = 55 + 0.15m −15 = −0.05m → m = 300 (not valid because >120).
So use constant price after day 120. Train diesel becomes constant at: 55 + 0.15×120 = 55 + 18 = 73.
Now set bus diesel = 73: 40 + 0.2m = 73 0.2m = 33 m = 165.
Day 165 of 2021: Jan (31) → 31 Feb (28) → 59 Mar (31) → 90 Apr (30) → 120 May (31) → 151 Day 165 is 14 days into June → 14 June.
• Question 2 of 5 2. Question There are eleven consecutive even numbers. If 56 is the mean of the first five such numbers, what is the mean of all the eleven numbers? (a) 58 (b) 60 (c) 62 (d) 64 Correct Answer: (c) Solution: Let the even numbers be: Mean of first five numbers is 56: Thus numbers are: 52, 54, 56, …, 72 Mean of all eleven numbers: Hence option (c) 62 is correct. Incorrect Answer: (c) Solution: Let the even numbers be: Mean of first five numbers is 56: Thus numbers are: 52, 54, 56, …, 72 Mean of all eleven numbers: Hence option (c) 62 is correct.
#### 2. Question
There are eleven consecutive even numbers. If 56 is the mean of the first five such numbers, what is the mean of all the eleven numbers?
Answer: (c)
Solution:
Let the even numbers be:
Mean of first five numbers is 56:
Thus numbers are:
52, 54, 56, …, 72
Mean of all eleven numbers:
Hence option (c) 62 is correct.
Answer: (c)
Solution:
Let the even numbers be:
Mean of first five numbers is 56:
Thus numbers are:
52, 54, 56, …, 72
Mean of all eleven numbers:
Hence option (c) 62 is correct.
• Question 3 of 5 3. Question Following is a matrix of certain entries. The entries follow a certain trend row-wise. Choose the missing entry (?) accordingly. 5X 8Y 3Z 3Z 10X 7Y 10X 15Z ? (a) 4Y (b) 5Y (c) 7X (d) 3X Correct Answer: (b) Solution: Again, observe each row: Row 1: Row 2: So the pattern is: (2nd entry) − (1st entry) = (3rd entry) Apply this to Row 3: Row 3: Numerical part: . Letter sequence across rows cycles as . For Row 3 the third position corresponds to Y. So the missing entry = 5Y. Hence, option (b) 5Y is correct. Incorrect Answer: (b) Solution: Again, observe each row: Row 1: Row 2: So the pattern is: (2nd entry) − (1st entry) = (3rd entry) Apply this to Row 3: Row 3: Numerical part: . Letter sequence across rows cycles as . For Row 3 the third position corresponds to Y. So the missing entry = 5Y. Hence, option (b) 5Y is correct.
#### 3. Question
Following is a matrix of certain entries. The entries follow a certain trend row-wise. Choose the missing entry (?) accordingly.
Answer: (b)
Solution:
Again, observe each row:
So the pattern is:
(2nd entry) − (1st entry) = (3rd entry)
Apply this to Row 3:
Numerical part: . Letter sequence across rows cycles as . For Row 3 the third position corresponds to Y.
So the missing entry = 5Y.
Hence, option (b) 5Y is correct.
Answer: (b)
Solution:
Again, observe each row:
So the pattern is:
(2nd entry) − (1st entry) = (3rd entry)
Apply this to Row 3:
Numerical part: . Letter sequence across rows cycles as . For Row 3 the third position corresponds to Y.
So the missing entry = 5Y.
Hence, option (b) 5Y is correct.
• Question 4 of 5 4. Question A and B can complete a task in 3 days and 4 days respectively. Work starts on Monday. A works on Day 1, B works on Day 2, and both work together on Day 3. This 3-day pattern then repeats (A alone, B alone, both together, …). Consider the following statements: The work will be finished on Wednesday. B works for fewer days than A. Which of the statements given above is/are correct? (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2 Correct Answer: (a) Explanation: A’s 1-day work = 1/3, B’s 1-day work = 1/4. In first 3 days: Day 1 (Mon): A → 1/3 Day 2 (Tue): B → +1/4 → total = 1/3 + 1/4 = 7/12 Day 3 (Wed): A + B → 1/3 + 1/4 = 7/12 Total after 3 days = 7/12 + 7/12 = 14/12 > 1. So the work finishes during Wednesday (Day 3). Statement 1 is correct. Up to completion, days worked: A: Day 1 and part of Day 3 → 2 days (effectively) B: Day 2 and part of Day 3 → 2 days (effectively) They both work the same number of days; so Statement 2 (“B works fewer days than A”) is false. Hence, only Statement 1 is correct → option (a). Incorrect Answer: (a) Explanation: A’s 1-day work = 1/3, B’s 1-day work = 1/4. In first 3 days: Day 1 (Mon): A → 1/3 Day 2 (Tue): B → +1/4 → total = 1/3 + 1/4 = 7/12 Day 3 (Wed): A + B → 1/3 + 1/4 = 7/12 Total after 3 days = 7/12 + 7/12 = 14/12 > 1. So the work finishes during Wednesday (Day 3). Statement 1 is correct. Up to completion, days worked: A: Day 1 and part of Day 3 → 2 days (effectively) B: Day 2 and part of Day 3 → 2 days (effectively) They both work the same number of days; so Statement 2 (“B works fewer days than A”) is false. Hence, only Statement 1 is correct → option (a).
#### 4. Question
A and B can complete a task in 3 days and 4 days respectively. Work starts on Monday. A works on Day 1, B works on Day 2, and both work together on Day 3. This 3-day pattern then repeats (A alone, B alone, both together, …).
Consider the following statements:
• The work will be finished on Wednesday.
• B works for fewer days than A.
Which of the statements given above is/are correct?
• (a) 1 only
• (b) 2 only
• (c) Both 1 and 2
• (d) Neither 1 nor 2
Answer: (a)
Explanation: A’s 1-day work = 1/3, B’s 1-day work = 1/4.
In first 3 days:
• Day 1 (Mon): A → 1/3
• Day 2 (Tue): B → +1/4 → total = 1/3 + 1/4 = 7/12
• Day 3 (Wed): A + B → 1/3 + 1/4 = 7/12
Total after 3 days = 7/12 + 7/12 = 14/12 > 1.
So the work finishes during Wednesday (Day 3). Statement 1 is correct.
Up to completion, days worked:
• A: Day 1 and part of Day 3 → 2 days (effectively)
• B: Day 2 and part of Day 3 → 2 days (effectively)
They both work the same number of days; so Statement 2 (“B works fewer days than A”) is false.
Hence, only Statement 1 is correct → option (a).
Answer: (a)
Explanation: A’s 1-day work = 1/3, B’s 1-day work = 1/4.
In first 3 days:
• Day 1 (Mon): A → 1/3
• Day 2 (Tue): B → +1/4 → total = 1/3 + 1/4 = 7/12
• Day 3 (Wed): A + B → 1/3 + 1/4 = 7/12
Total after 3 days = 7/12 + 7/12 = 14/12 > 1.
So the work finishes during Wednesday (Day 3). Statement 1 is correct.
Up to completion, days worked:
• A: Day 1 and part of Day 3 → 2 days (effectively)
• B: Day 2 and part of Day 3 → 2 days (effectively)
They both work the same number of days; so Statement 2 (“B works fewer days than A”) is false.
Hence, only Statement 1 is correct → option (a).
• Question 5 of 5 5. Question If 6 persons take 9 hours to pack 18 boxes, how many hours will 3 persons take to pack 6 boxes, assuming all persons and boxes are identical? (a) 3 (b) 6 (c) 9 (d) 12 Correct Answer: (b) Explanation: 6 persons pack 18 boxes in 9 hours. Total work = 6 × 9 = 54 person-hours This is for 18 boxes. Work per box = 54 / 18 = 3 person-hours per box For 6 boxes: Required work = 6 × 3 = 18 person-hours With 3 persons: Time = 18 / 3 = 6 hours Hence, option (b) is correct. Incorrect Answer: (b) Explanation: 6 persons pack 18 boxes in 9 hours. Total work = 6 × 9 = 54 person-hours This is for 18 boxes. Work per box = 54 / 18 = 3 person-hours per box For 6 boxes: Required work = 6 × 3 = 18 person-hours With 3 persons: Time = 18 / 3 = 6 hours Hence, option (b) is correct.
#### 5. Question
If 6 persons take 9 hours to pack 18 boxes, how many hours will 3 persons take to pack 6 boxes, assuming all persons and boxes are identical?
Answer: (b)
Explanation:
6 persons pack 18 boxes in 9 hours.
Total work = 6 × 9 = 54 person-hours This is for 18 boxes.
Work per box = 54 / 18 = 3 person-hours per box
For 6 boxes: Required work = 6 × 3 = 18 person-hours
With 3 persons: Time = 18 / 3 = 6 hours
Hence, option (b) is correct.
Answer: (b)
Explanation:
6 persons pack 18 boxes in 9 hours.
Total work = 6 × 9 = 54 person-hours This is for 18 boxes.
Work per box = 54 / 18 = 3 person-hours per box
For 6 boxes: Required work = 6 × 3 = 18 person-hours
With 3 persons: Time = 18 / 3 = 6 hours
Hence, option (b) is correct.
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