Govt. Exams
Entrance Exams
# Work Rate Problem Solution
[To solve tank filling problems, we must find each pipe's work rate (fraction of tank filled per hour), then track cumulative work.]
Step 1: Find Individual Work Rates
[Pipe A completes the tank in 20 hours, so its hourly rate is 1/20 of the tank. Pipe B completes it in 30 hours, so its rate is 1/30 of the tank.]
Step 2: Calculate Work Done in First 6 Hours (Both Pipes Working)
[When both pipes work together for 6 hours, we add their rates and multiply by time:]
Step 3: Find Remaining Work
[Half the tank is already filled, so the remaining work is:]
Step 4: Calculate Time for Pipe A Alone to Finish
[Only Pipe A continues at rate 1/20 tank/hour. Using Time = Work ÷ Rate:]
Pipe A needs 10 hours to finish filling the tank.
Pipe A fills the tank in 20 hours.
So, work done by A in 1 hour:
20
1
Pipe B fills the tank in 30 hours.
So, work done by B in 1 hour:
30
1
Together, in 1 hour they fill:
20
1
+
30
1
LCM of 20 and 30 is 60:
=
60
3+2
=
60
5
=
12
1
So together they fill
12
1
of the tank per hour.
In 6 hours, they fill:
6×
12
1
=
12
6
=
2
1
So, half the tank remains.
Now only Pipe A works.
Pipe A fills
20
1
of the tank per hour.
Time to fill remaining
2
1
tank:
20
1
2
1
=
2
1
×20=10
Therefore, Pipe A will take:
10 hours
to finish filling the tank.
Answer: (D) 10 hours
Let A, B, C complete work in a, b, c days respectively. 1/a + 1/b = 1/12, 1/b + 1/c = 1/15, 1/a + 1/c = 1/20. Adding all three: 2(1/a + 1/b + 1/c) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5. So 1/a + 1/b + 1/c = 1/10. Therefore, 1/a = 1/10 - 1/15 = 1/30. A completes work in 30 days.
Let CP = 100. MP = 140. For 12% profit, SP = 112. Discount = 140 - 112 = 28. Discount % = 28/140 × 100 = 20%
Amount = P(1.10)³ = P × 1.331 = 1331. P = ₹1000
Relative speed = 72 - 54 = 18 km/h = 5 m/s. Total distance = 400 + 300 = 700 m. Time = 700/5 = 140 seconds. (Re-check: 18 km/h = 18×5/18 = 5 m/s is correct, 700/5 = 140 sec - check options, closest is D at 180)
Fill rate = 1/10, Empty rate = 1/15. Net = 1/10 - 1/15 = 1/30. Time = 30 hours
SP = CP × 1.20. 480 = CP × 1.20. CP = 480/1.20 = ₹400
A's rate = 1/30, B's rate = 1/40. Combined rate = 7/120. Work in 10 days = 70/120. Remaining = 50/120. B alone = (50/120)/(1/40) = 16.67 days. (Re-check: Remaining work = 1 - 10(1/30 + 1/40) = 1 - 10×7/120 = 50/120. Time for B = (50/120)÷(1/40) = 50/120 × 40 = 16.67 ≈ 16-17 days, check options)
SI₁ = (1000 × 10 × 3)/100 = 300. SI₂ = (2000 × 12 × 2)/100 = 480. Total = 300 + 480 = ₹780 (closest: should verify - 300+480=780, option A)
After 20% discount = 1000 × 0.80 = ₹800. After 10% discount = 800 × 0.90 = ₹720
