Maths-3 Advanced practice questions on Pipes & Cisterns and Wages Distribution, with answers and explanations for Competitive Exams (SSC, BSSC, Bank,Railways)

Maths-3 Advanced practice questions on Pipes & Cisterns and Wages Distribution, with answers and explanations for Competitive Exams {SSC, BSSC, Bank,Railways)

Maths-3 Advanced practice

Pipes and Cisterns

1. Pipe A fills a tank in 6 hours. Pipe B fills it in 4 hours. How long will both take together?
Solution:
Rate = 1/6 + 1/4 = 5/12 → Time = 12/5 = 2.4 hours

2. Pipe A fills in 5 hours, Pipe B empties in 10 hours. Both opened together. Time to fill tank?
Solution:
Rate = 1/5 – 1/10 = 1/10 → Time = 10 hours

3. Pipe A fills in 3 hours, Pipe B fills in 6 hours, Pipe C empties in 9 hours. All opened together.
Solution:
Rate = 1/3 + 1/6 – 1/9 = (6 + 3 – 2)/18 = 7/18 → Time = 2.57 hours

4. A fills in 4 hrs, B empties in 6 hrs. If both opened together, how long to fill tank?
Solution:
Rate = 1/4 – 1/6 = 1/12 → Time = 12 hours

5. A fills in 8 hrs, B fills in 12 hrs. C empties in 24 hrs. All opened together.
Solution:
Rate = 1/8 + 1/12 – 1/24 = (3 + 2 – 1)/24 = 4/24 = 1/6 → Time = 6 hours

6. A fills in 2 hrs, B fills in 3 hrs. C empties in 6 hrs. All opened together.
Solution:
Rate = 1/2 + 1/3 – 1/6 = (3 + 2 – 1)/6 = 4/6 = 2/3 → Time = 1.5 hours

7. A fills in 10 hrs, B empties in 15 hrs. If tank is half full, how long to fill completely?
Solution:
Rate = 1/10 – 1/15 = 1/30
Remaining work = 1/2 → Time = 1/2 ÷ 1/30 = 15 hours

8. A fills in 5 hrs, B fills in 10 hrs. C empties in 20 hrs. All opened together.
Solution:
Rate = 1/5 + 1/10 – 1/20 = (4 + 2 – 1)/20 = 5/20 = 1/4 → Time = 4 hours

9. A fills in 6 hrs, B empties in 9 hrs. If tank is 1/3 full, how long to fill completely?
Solution:
Rate = 1/6 – 1/9 = 1/18
Remaining = 2/3 → Time = 2/3 ÷ 1/18 = 12 hours

10. A fills in 4 hrs, B fills in 5 hrs, C empties in 20 hrs. All opened together.
Solution:
Rate = 1/4 + 1/5 – 1/20 = (5 + 4 – 1)/20 = 8/20 = 2/5 → Time = 2.5 hours

Wages Distribution

11. A can do a job in 10 days, B in 5 days. Total wage = ₹900. How much does A get?
Solution:
Efficiency = 1:2 → A gets ₹300

12. A = 12 days, B = 18 days, C = 36 days. Wage = ₹1080. Share of B?
Solution:
Efficiency = 3:2:1 → B gets ₹360

13. A and B work together. A works 6 days, B works 4 days. A = 2 units/day, B = 3 units/day. Wage = ₹1000.
Solution:
A = 12 units, B = 12 units → Equal share = ₹500 each

14. A = 10 days, B = 20 days, C = 40 days. Wage = ₹1200. Share of C?
Solution:
Efficiency = 4:2:1 → C gets ₹171.43

15. A = 6 days, B = 3 days. Wage = ₹600. Share of B?
Solution:
Efficiency = 1/6 : 1/3 = 1 : 2 → B gets ₹400

16. A = 5 days, B = 10 days. Wage = ₹900. Share of A?
Solution:
Efficiency = 2:1 → A gets ₹600

17. A = 8 days, B = 12 days, C = 24 days. Wage = ₹960. Share of A?
Solution:
Efficiency = 3:2:1 → A gets ₹480

18. A = 15 days, B = 10 days. Wage = ₹750. Share of B?
Solution:
Efficiency = 1/15 : 1/10 = 2:3 → B gets ₹450

19. A = 9 days, B = 6 days, C = 3 days. Wage = ₹600. Share of C?
Solution:
Efficiency = 1:1.5:3 → Ratio = 2:3:6 → C gets ₹300

20. A = 20 days, B = 10 days, C = 5 days. Wage = ₹1050. Share of B?
Solution:
Efficiency = 1:2:4 → B gets ₹300

These are a few advanced practice questions on Pipes & Cisterns and Wages Distribution. To master the technique, one needs to practice at least 20 questions every day. Maths is all about practice.