Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
P, Q and R can fill a tank in 9 hours, 18 hours and 12 hours, respectively. They start the work i.e. filling the tank, with P working on hour 1, Q working on hour 2 and R working on hour 3, and then continuing with this cycle till the work is completed. How many hours will be needed to complete this work in this manner?
16 hours
11 hours
12 hours
15 hours
12 hours
Calculate the total work as the LCM (9, 18, 12) = 36 units. In one 3-hour cycle, the work done is 4 + 2 + 3 = 9 units. Since 36/9 = 4, there are 4 full cycles, each taking 3 hours, thus 4 × 3 = 12 hours.
P fills in 9 hours, Q in 18 hours, R in 12 hours. They work in a cyclic order: P (1st hour), Q (2nd hour), R (3rd hour).
Total Work=Efficiency×Time
Calculate the total work as the LCM (9, 18, 12) = 36 units. In one 3-hour cycle, the work done is 4 + 2 + 3 = 9 units. Since 36/9 = 4, there are 4 full cycles, each taking 3 hours, thus 4 × 3 = 12 hours.
Students often miscalculate the work per cycle or confuse the hourly rotation, failing to realize that the work completes exactly at the end of the 4th cycle.
Calculate Efficiencies
Assuming total tank capacity is the LCM of 9, 18, and 12, which is 36 units. The hourly capacities are EP=36/9=4 units/hr, EQ=36/18=2 units/hr, and ER=36/12=3 units/hr.
EP=4,EQ=2,ER=3
Determine Cycle Work
In one cycle of 3 hours (P, then Q, then R), total work done is 4+2+3=9 units.
Workcycle=9 units/cycle
Calculate Total Cycles
Since total work is 36 units and each cycle does 9 units, the number of cycles required is 36/9=4 cycles.
Cycles=936=4
Calculate Total Time
Each cycle lasts 3 hours, so 4 cycles take 4×3=12 hours.
Time=4×3=12 hours
C is correct because the total work of 36 units is finished exactly at the end of 4 cycles, which corresponds to 12 hours.
This rotational work pattern is similar to problems involving alternating laborers; always calculate the work per complete cycle first to determine the number of iterations.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants