Given:
A's time = 9 days for 3/4th work,
B's time = 12 days for 2/5th work,
A + B + C's time = 60/11 days,
Total earnings = Rs. 330
Concept:
Shares of A, B, C are proportional to the amount of work they did in the given time
Calculation:
Calculate the total shares of A, B, and C.
Time taken by A to complete the whole work = 9 × 4/3 = 12 days
Time taken by B to complete the whole work = 12 × 5/2 = 30 days
Time taken by all three = 60/11 days
LCM of 12, 30, and 60/11 = 60
So, Let the total work be 60 units
Efficiency of A = 60/12 = 5
Efficiency of B = 60/30 = 2
Efficiency of all three = 60/(60/11) = 11
Efficiency of C = Eff.(A+B+C) - Eff.(A + B)
⇒ Efficiency of C = 11 - (5+2)
⇒ 11 - 7 = 4
Thus, Efficiency of C = 4 units
Now, the amount of work done by A in 60/11 days ⇒ 5 × 60/11 = 300/11
The amount of work done by B in 60/11 days ⇒ 2 × 60/11 = 120/11
The amount of work done by C in 60/11 days ⇒ 4 × 60/11 = 240/11
Ratio of work done of A, B, and C =300/11 : 120/11 : 240/11 = 5 : 2 : 4
Since, Total shares = Sum of the ratio of work done,
So, Sum of ratio of work done = 5 + 2 + 4 = 11 units
⇒ Total shares = 11 units
⇒ 330 = 11 units
⇒ 1 unit = 30
⇒ A's share = 30 × 5 = Rs. 150
⇒ C's share = 30 × 4 = Rs. 120
The difference in the share of A and C = 150 - 120
⇒ Rs. 30
∴ The correct answer is Rs. 30