Working alone A can do the task in 27 hours and B can do it in 54 hours. Find share if A, B and C get paid Rs. 4,320 for completing the task in 12 hours on which they worked together?
a) 1440 Rs.
b) 960 Rs.
c) 1920 Rs.
d) 1280 Rs.
Sol:
Let’s take Total task = 108 units (LCM of 27, 54 and 12)
⇒ Task completed in 1 hour by A = 108/27 = 4 units
⇒ Task completed in 1 hour by B = 108/54 = 2 units
⇒ Task completed in 1 hour by A, B and C together = 108/12 = 9 units
⇒ Task completed by C in 1 hour will be = 9 – 4 – 2 = 3 units
⇒ Number of hours C will take to complete the task = Total task/Task completed in one hour = 108/3 = 36 hours
⇒ Ratio of no. of hours taken by A, B and C = 27 : 54 ∶ 36 = 3 ∶ 6 ∶ 4
⇒ Ratio of efficiencies of A, B and C = 4 : 2 : 3
Since the amount will be distributed according to efficiency,
∴ Amount received by C = 3/9 × 4320 = Rs. 1440
30.
