Maths-3: Advanced Time and Work concept with step by step solutions for Competitive Exams SSC,BSSC,Bank, Railways

Maths-3: Advanced Time and Work concept swith step by step solutions for Competitive Exams SSC,BSSC,Bank, Railways

Advanced Time and Work concepts –starting with Pipes and Cisterns and then moving to Wages Distribution. These topics are extensions of basic Time and Work, but with a twist.

Advanced Time and Work concepts

Pipes and Cisterns

🔹 Core Concept

• Inlet pipe: Fills the tank → Positive work
• Outlet pipe: Empties the tank → Negative work

🔹 Basic Formula

• If a pipe fills a tank in x hours → Rate = 1/x
• If a pipe empties a tank in y hours → Rate = –1/y
• Net rate = Sum of all rates
• Time to fill/empty = 1 ÷ Net rate

Example 1: One Inlet, One Outlet

Q: Pipe A fills in 6 hrs, Pipe B empties in 12 hrs. How long to fill the tank?

Solution:
Rate = 1/6 – 1/12 = (2 – 1)/12 = 1/12
Time = 1 ÷ (1/12) = 12 hrs

Example 2: Two Inlets

Q: Pipe A fills in 4 hrs, Pipe B in 6 hrs. How long together?

Solution:
Rate = 1/4 + 1/6 = (3 + 2)/12 = 5/12
Time = 1 ÷ (5/12) = 2.4 hrs

Example 3: Alternate Filling and Emptying

Q: A fills in 3 hrs, B empties in 4 hrs. If both opened together?

Solution:
Rate = 1/3 – 1/4 = (4 – 3)/12 = 1/12
Time = 12 hrs

Shortcut Tip

If A fills in x hrs and B empties in y hrs:
Net time = (x × y)/(y – x) (if y > x)

Wages Distribution

🔹 Core Concept

• Wages are distributed in proportion to work done
• Work done ∝ Efficiency ∝ Time worked

Example 1: Equal Time, Different Efficiency

Q: A can do a job in 10 days, B in 5 days. Total wage = ₹900. How to divide?

Solution:
Efficiency: A = 1/10, B = 1/5 → Ratio = 1:2
Total parts = 3 → A gets ₹300, B gets ₹600

Example 2: Different Time Worked

Q: A and B work together. A works 6 days, B works 4 days. A’s efficiency = 2 units/day, B = 3 units/day. Total wage = ₹1000.

Solution:
A’s work = 6 × 2 = 12 units
B’s work = 4 × 3 = 12 units
Equal work → ₹500 each

Example 3: Three Workers

Q: A, B, C work together. A = 10 days, B = 15 days, C = 30 days. Total wage = ₹1080.

Solution:
Efficiency: A = 3, B = 2, C = 1 (LCM = 30)
Ratio = 3:2:1 → Total parts = 6
A = ₹540, B = ₹360, C = ₹180