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Question 1 of 5
1. Question
Three masons Arav, Bala and Charu are to plaster a long boundary wall. Working independently, they can complete the whole work in 18, 27 and 54 days, respectively. Arav alone works on Monday, Bala alone works on Tuesday, Charu alone works on Wednesday, Arav again on Thursday, and so on (the trio keeps repeating in that order). Consider the statements:
(I) The work will be finished on Sunday.
(II) The work will be finished in 27 days.Which of the above statement(s) is/are correct?
Correct
Ans: (c)
Explanation:
Take total work = LCM(18, 27, 54) = 54 units.
Daily efficiencies: Arav = 54/18 = 3 units/day, Bala = 54/27 = 2 units/day, Charu = 54/54 = 1 unit/day.
A 3‑day block (Mon–Wed) completes 3 + 2 + 1 = 6 units.
Total blocks needed = 54/6 = 9 blocks = 27 days.
Starting on Monday, day 7 is Sunday, day 14 is Sunday, day 21 is Sunday, day 27 is Sunday.
So it finishes on Sunday and in 27 days. Hence, both statements are correct.Incorrect
Ans: (c)
Explanation:
Take total work = LCM(18, 27, 54) = 54 units.
Daily efficiencies: Arav = 54/18 = 3 units/day, Bala = 54/27 = 2 units/day, Charu = 54/54 = 1 unit/day.
A 3‑day block (Mon–Wed) completes 3 + 2 + 1 = 6 units.
Total blocks needed = 54/6 = 9 blocks = 27 days.
Starting on Monday, day 7 is Sunday, day 14 is Sunday, day 21 is Sunday, day 27 is Sunday.
So it finishes on Sunday and in 27 days. Hence, both statements are correct. -
Question 2 of 5
2. Question
Pipe A can fill a tank in 8 hours, Pipe B can empty it in 12 hours, and Pipe C can fill it in 24 hours. All three are opened together at 10:00 a.m. After some time, Pipe B is closed, and the tank gets completely filled at 8:00 p.m. When was Pipe B closed?
Correct
Answer: (d)
Explanation:
A = 8 h (fill), B = 12 h (empty), C = 24 h (fill)
LCM = 24 units
Efficiency: A = 3 u/hr, B = –2 u/hr, C = 1 u/hr
With all three open: net = 3 – 2 + 1 = 2 u/hr
After closing B: net = 3 + 1 = 4 u/hr
Total time from 10 a.m. to 8 p.m. = 10 hours
Let B was open for x hours.
Total work = 24 units = (2 × x) + [4 × (10 – x)]
⇒ 24 = 2x + 40 – 4x = 40 – 2x ⇒ 2x = 16 ⇒ x = 8
So B was closed 8 hours after 10 a.m. ⇒ 6:00 p.m.
Hence, option (d) is correct.Incorrect
Answer: (d)
Explanation:
A = 8 h (fill), B = 12 h (empty), C = 24 h (fill)
LCM = 24 units
Efficiency: A = 3 u/hr, B = –2 u/hr, C = 1 u/hr
With all three open: net = 3 – 2 + 1 = 2 u/hr
After closing B: net = 3 + 1 = 4 u/hr
Total time from 10 a.m. to 8 p.m. = 10 hours
Let B was open for x hours.
Total work = 24 units = (2 × x) + [4 × (10 – x)]
⇒ 24 = 2x + 40 – 4x = 40 – 2x ⇒ 2x = 16 ⇒ x = 8
So B was closed 8 hours after 10 a.m. ⇒ 6:00 p.m.
Hence, option (d) is correct. -
Question 3 of 5
3. Question
A pack of 52 cards contains four different colors cards each color contains cards numbered from 1 to 13. Cards are drawn randomly from the pack. Consider the following statements:
- Smallest number of attempts, which will always get full set of atleast one color 49.
- Smallest number of attempts, which will always get atleast one card of each color is 40.
Which of the statements given above is/are correct?
Correct
Answer: (c)
Solution
Statement 1 is correct: For full set of one color we have to take the worst case. Worst case is one card of each color remaining in the pack till the last ie till we withdraw 48 cards. Next card withdraw is bound to fulfill atleast one set of color. So number of attempts is 49.
Statement 2 is correct: For getting at least one card of each color, i.e. getting all color cards, the worst case is one color is totally left out until others are drawn, i.e. 13 x 3 i.e. 39 cards are drawn. The next card i.e. 40 th card when we draw, it is bound to give atleast one cards of all color. Hence, option (c) is correct
Incorrect
Answer: (c)
Solution
Statement 1 is correct: For full set of one color we have to take the worst case. Worst case is one card of each color remaining in the pack till the last ie till we withdraw 48 cards. Next card withdraw is bound to fulfill atleast one set of color. So number of attempts is 49.
Statement 2 is correct: For getting at least one card of each color, i.e. getting all color cards, the worst case is one color is totally left out until others are drawn, i.e. 13 x 3 i.e. 39 cards are drawn. The next card i.e. 40 th card when we draw, it is bound to give atleast one cards of all color. Hence, option (c) is correct
-
Question 4 of 5
4. Question
The average temperature for the first four days of a week was 64°C. The average for the 2nd, 3rd, 4th, and 5th days was 66°C. If the ratio of the temperatures on the 1st and 5th days was 5:6, what was the temperature on the 1st day?
Correct
Answer: (d)
Explanation:
Let temps on 1st to 5th days be A, B, C, D, E.
From the question:
- A + B + C + D = 64 × 4 = 256
- B + C + D + E = 66 × 4 = 264
Subtract:
→ (B + C + D + E) − (A + B + C + D)
→ E − A = 8
Also, A : E = 5 : 6 ⇒ Let A = 5x, E = 6x
So, E − A = x = 8 ⇒ x = 8
⇒ A = 5x = 40Incorrect
Answer: (d)
Explanation:
Let temps on 1st to 5th days be A, B, C, D, E.
From the question:
- A + B + C + D = 64 × 4 = 256
- B + C + D + E = 66 × 4 = 264
Subtract:
→ (B + C + D + E) − (A + B + C + D)
→ E − A = 8
Also, A : E = 5 : 6 ⇒ Let A = 5x, E = 6x
So, E − A = x = 8 ⇒ x = 8
⇒ A = 5x = 40 -
Question 5 of 5
5. Question
A thief is spotted by a policeman 300 m ahead and runs at 8 m/s. The policeman starts chasing immediately at 12 m/s. After how much time will the policeman catch the thief?
Correct
Answer: (b)
Solution:
Initial gap = 300 m
Relative speed = 12 − 8 = 4 m/s
Time = 300 ÷ 4 = 75 seconds
So, option (b) is correct.Incorrect
Answer: (b)
Solution:
Initial gap = 300 m
Relative speed = 12 − 8 = 4 m/s
Time = 300 ÷ 4 = 75 seconds
So, option (b) is correct.
