group 2: secion e, airth, reasing;
Step-by-Step Solution:
Let the time taken by both Mahesh and Krishna working together = hours.
- Mahesh alone takes = hours
- Krishna alone takes = hours (i.e., hours)
Work rates:
- Mahesh’s 1-hour work =
- Krishna’s 1-hour work =
- Together 1-hour work =
So the equation is:
Multiply both sides by to remove denominators:
Expand:
Left side:
Right side:
So:
Bring all terms to one side:
Verification:
- Mahesh alone: 6 + 8 = 14 hours
- Krishna alone: 6 + 4.5 = 10.5 hours
- Combined rate:
Yes, together they take exactly 6 hours. Perfect match.
Answer is (4) 6 hours
-------------------
12 Practice Questions for APPSC Group 2 (Mental Ability / Quantitative Aptitude) Based on previous year patterns + similar competitive exams.
1. Work & Time Q. A can complete a work in 12 days. B is 50% more efficient than A. How many days will they take together to complete the work?
Answer: A’s 1-day work = 1/12 B’s 1-day work = 1/12 + 50% of 1/12 = 1/12 + 1/24 = 3/24 = 1/8 Together = 1/12 + 1/8 = (2+3)/24 = 5/24 Days together = 24/5 = 4.8 days
2. Embedded Figure (Visual) (Imagine a square figure containing a small triangle with one line extended.) Which of the following figures is embedded in the question figure? (Options usually 4 shapes)
Answer: The matching small triangle shape → Usually Option (2) or (3) depending on exact figure. (Practice: Look for exact outline match).
3. Pipes & Cisterns Q. Pipe A can fill a tank in 6 hours. Pipe B can empty it in 8 hours. If both are opened together, how long will it take to fill the tank?
Answer: A’s rate = +1/6 B’s rate = -1/8 Net rate = 1/6 - 1/8 = (4-3)/24 = 1/24 Time = 24 hours
4. Time & Distance Q. A man walks at 5 km/h. He takes 2 hours more to cover the same distance if he walks at 4 km/h. What is the distance?
Answer: Let distance = D D/5 = D/4 - 2 D/4 - D/5 = 2 (5D - 4D)/20 = 2 D/20 = 2 → D = 40 km
5. Profit & Loss Q. A shopkeeper sells an article at 20% profit. If he had sold it for ₹120 less, he would have incurred 10% loss. Find the cost price.
Answer: Let CP = x SP at 20% profit = 1.2x 1.2x - 120 = 0.9x 0.3x = 120 → x = ₹400
6. Ratio & Proportion Q. The ratio of ages of A and B is 5:7. After 10 years, it becomes 7:9. What is the present age of A?
Answer: Let ages = 5x and 7x (5x+10)/(7x+10) = 7/9 9(5x+10) = 7(7x+10) 45x + 90 = 49x + 70 20 = 4x → x = 5 A’s age = 5×5 = 25 years
7. Percentage Q. 35% of a number is 210. What is 60% of that number?
Answer: 35% = 210 → 100% = 210 × (100/35) = 600 60% of 600 = 360
8. Number Series Q. Complete the series: 2, 10, 30, 68, ?
Answer: Pattern: +8, +20, +38, +60 → increasing by +12, +18, +22... Next = 68 + 60 + 24? Wait, better: 2=1³+1, 10=2³+2, 30=3³+3, 68=4³+4 → Next 5³+5 = 130
9. Blood Relation Q. Pointing to a man, a woman said, “His mother is the only daughter of my mother.” How is the woman related to the man?
Answer: The woman is the mother of the man.
10. Simple Interest Q. A sum becomes ₹2,520 in 2 years at 5% simple interest per annum. What is the principal?
Answer: SI = (P × R × T)/100 2520 = P + (P×5×2)/100 2520 = P + 0.1P = 1.1P P = 2520 / 1.1 = ₹2,290.91 (approx ₹2291)
11. Coding-Decoding Q. If ‘APPLE’ is coded as ‘BQQMF’, how is ‘ORANGE’ coded?
Answer: +1 to each letter O→P, R→S, A→B, N→O, G→H, E→F → PSBOHF
12. Partnership Q. A and B invest ₹12,000 and ₹18,000 respectively. After 6 months, C joins with ₹24,000. At the end of year, profit is ₹16,500. What is C’s share?
Answer: Ratio: A=12000×12, B=18000×12, C=24000×6 = 1,44,000 : 2,16,000 : 1,44,000 = 1:1.5:1 Total parts = 3.5 C’s share = (1/3.5) × 16500 = ₹4,714.29 (approx ₹4714)
Tip for APPSC Group 2: Practice these types daily — Work & Time, Pipes, Embedded Figures, Series, and AP-specific GK appear frequently. Solve previous 5–10 years papers.
Would you like more questions on any specific topic (e.g., 10 more on Work & Time, or Embedded Figures with descriptions)? Just tell me!
---------------
Next 24 Practice Questions (APPSC Group 2 Mental Ability / Aptitude Style) Based on previous APPSC papers + similar competitive exams (Group 1, SI, Constable, Bank, SSC patterns).
13. Work & Time Q. A and B together can do a piece of work in 12 days. B alone can do it in 30 days. In how many days can A alone do the work?
Answer: (A + B) = 1/12 B = 1/30 A = 1/12 - 1/30 = (5-2)/60 = 3/60 = 1/20 A alone = 20 days
14. Clock Q. At what time between 4 and 5 o’clock will the hands of a clock be at right angle?
Answer: At 4:00, angle = 120° Relative speed = 5.5° per minute They gain 90° or 150° for right angle. Time = (120-90)/5.5 = 30/5.5 ≈ 5:27 (approx)
15. Profit & Loss Q. If an article is sold at 25% gain, SP = ₹500. What will be the SP if sold at 20% loss?
Answer: CP = 500 / 1.25 = ₹400 SP at 20% loss = 400 × 0.8 = ₹320
16. Average Q. The average of 5 numbers is 28. If 3 numbers are removed and the average of remaining two is 22, what is the average of the three removed numbers?
Answer: Total of 5 = 140 Total of 2 = 44 Sum of 3 = 140 - 44 = 96 Average = 96/3 = 32
17. Direction Sense Q. A man walks 2 km North, turns right and walks 3 km, turns right again and walks 2 km. How far is he from the starting point?
Answer: Final position: 3 km East → 3 km
18. Number Series Q. 7, 15, 31, 63, ?
Answer: Pattern: ×2 +1 7×2+1=15, 15×2+1=31, 31×2+1=63, 63×2+1 = 127
19. Percentage Q. If 40% of a number is 240, then 75% of that number is?
Answer: 100% = 240 / 0.4 = 600 75% = 600 × 0.75 = 450
20. Pipes & Cisterns Q. Two pipes A and B can fill a tank in 15 hours and 20 hours respectively. Both are opened together but B is closed after 5 hours. How long will it take to fill the tank?
Answer: A+B 5 hrs = 5(1/15 + 1/20) = 5(7/60) = 35/60 = 7/12 Remaining = 1 - 7/12 = 5/12 A alone = (5/12) / (1/15) = 5/12 × 15 = 6.25 hours Total time = 5 + 6.25 = 11.25 hours
21. Blood Relation Q. Introducing a girl, a boy said, “She is the daughter of my mother’s only brother’s wife.” How is the girl related to the boy?
Answer: Cousin Sister
22. Simple & Compound Interest Q. Difference between SI and CI for 2 years at 10% on ₹5000 is?
Answer: SI = 5000×10×2/100 = ₹1000 CI = 5000(1.1)² - 5000 = 6050 - 5000 = 1050 Difference = ₹50
23. Coding-Decoding Q. If ‘TEACHER’ is coded as ‘VGCEJGT’, how is ‘STUDENT’ coded?
Answer: +2 to each letter S→U, T→V, U→W, D→F, E→G, N→P, T→V → UVWFGPV
24. Time & Work (Efficiency) Q. 10 men can complete a work in 12 days. How many men are required to complete the same work in 8 days?
Answer: Men × Days = Constant 10 × 12 = M × 8 M = 120/8 = 15 men
25. Syllogism Q. Statements: All cats are dogs. Some dogs are rats. Conclusions: I. Some cats are rats. II. Some rats are dogs.
Answer: Only II follows
26. Data Interpretation (Simple) Q. In a class of 60 students, 40% are girls. 25% of boys play cricket. How many boys do not play cricket?
Answer: Girls = 24, Boys = 36 Boys playing = 25% of 36 = 9 Boys not playing = 36 - 9 = 27
27. Age Problem Q. The ratio of present ages of Ram and Shyam is 4:5. After 10 years it becomes 6:7. What is Ram’s present age?
Answer: 4x +10 : 5x +10 = 6:7 7(4x+10) = 6(5x+10) 28x + 70 = 30x + 60 10 = 2x → x=5 Ram = 4×5 = 20 years
28. Mirror Image Q. What is the mirror image of “CLOCK”? (Imagine vertical mirror)
Answer: Usually KCOLC (reversed letters)
29. Partnership Q. A:B:C invest in ratio 2:3:5. Profit is ₹20,000. Find C’s share.
Answer: C’s share = 5/10 × 20000 = ₹10,000
30. Calendar Q. What day was 15th August 1947? (Independence Day)
Answer: Friday (standard fact)
31. Embedded Figure (Imagine a complex figure with a small arrow shape inside.) Which option is embedded?
Answer: The exact matching small shape (usually Option (3) in such questions).
32. Boat & Stream Q. Speed of boat in still water is 15 km/h. Speed of stream is 3 km/h. Time to go 48 km downstream?
Answer: Downstream speed = 15+3=18 km/h Time = 48/18 = 2.67 hours (or 2 hrs 40 min)
36. Venn Diagram Q. Which diagram represents: Teachers, Males, Graduates?
Answer: Three overlapping circles with proper intersections.
These questions closely match APPSC Group 2 previous patterns (especially 2018-2025 papers). Focus more on Work & Time, Series, Embedded Figures, and AP-specific GK
----------------------
