A, B and C working separately can do a piece of work in 5, 8 and 6 days, respectively. If they all work together and earn Rs. 22,774 for the whole work, then find the difference between the shares of B and C.

Correct option is A

Given:
A can do the work in 5 days
B can do the work in 8 days
C can do the work in 6 days
Total earnings = Rs. 22,774
Formula Used:
Work share is proportional to efficiency
Efficiency = 1 ÷ Time taken
Share of a person = (Efficiency of person ÷ Total Efficiency) × Total Earnings
Solution:
Efficiency of A = $$\frac 15$$​, B = $$\frac 18$$​, C = $$\frac 16$$​​
LCM of 5, 8, 6 = 120 (take as total work)
A’s work = 120 ÷ 5 = 24
B’s work = 120 ÷ 8 = 15
C’s work = 120 ÷ 6 = 20
Total work = 24 + 15 + 20 = 59
​$$\text{B's share} = \left(\dfrac{15}{59}\right) \times 22774 = 5790 \\ \text{C's share} = \left(\dfrac{20}{59}\right) \times 22774 = 7720$$​​
Difference = 7720 − 5790 = 1930