To do a certain work, the ratio of the efficiencies of A, B and C is 7 : 5 : 6. Working together, they can complete the same work in 35 days. B and C work together for 21 days. The remaining work will be completed by A alone in:

57

The efficiencies of A, B and C is    7 : 5 : 6 

Let the efficiencies  of A,B and C be equal to 7,5 and 6 unit/day respectively.

Total work = Efficiency  ×  Number of days 

total work done by ( A + B + C ) together in 1 day = (7+5+6) = 18 units

Number of days = 35 days 

Total work = 18  × 35 = 630 units 

work done by ( B + C ) in 1 day = 11 unit 

work done by ( B + C ) in 21 days = 11 × 21 = 231 unit 

Remaining work = 600 - 231 = 399 units

Hence, time taken by A alone  yo do remaining work = \(\frac{399}{7}\) = 57 days