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:

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

(A+B+C)' s working together can complete the work in 35 days is 

= $$\frac{1}{x÷7}$$+  $$\frac{1}{x÷5}$$+ $$\frac{1}{x÷6}$$ = $$\frac{1}{35}$$

= $$\frac{7}{x}$$ +  $$\frac{5}{x}$$ +  $$\frac{6}{x}$$ = $$\frac{1}{35}$$

  $$\frac{18}{x}$$ = $$\frac{1}{35}$$

x=630

B work is = $$\frac{5}{x}$$ = $$\frac{5}{630}$$ = $$\frac{1}{126}$$

C work is = $$\frac{6}{x}$$ = $$\frac{6}{630}$$ = $$\frac{1}{105}$$

(B+C)' 1 days work =  $$\frac{1}{126}$$+ $$\frac{1}{105}$$

Take the orderes of 105 and 126 is 630 hence

= $$\frac{5+6}{630}$$ 

= $$\frac{11}{630}$$

21 days work of (B+C) = $$\frac{11}{630}$$ ×21

= $$\frac{11}{30}$$

Remaining work = 1- $$\frac{11}{30}$$

Remaining work = $$\frac{19}{30}$$

A's 1 days work = $$\frac{7}{x}$$ = $$\frac{7}{630}$$ = $$\frac{1}{90}$$

A's 1 days work = $$\frac{1}{90}$$

The remaining work will be completed by A alone in = $$\frac{19}{30}$$ ×90

y=57 days