Question

OULU 33. A,B and C can do a work separately in 16, 32 and 48 days, respectively, They started the work together but B leaving off 8 days and C, 6 days before the completion of the work. In what time is the work finished? (1) 10 days (2) 12 days (3) 14 days (4) 9 days

11th - 12th Class

Maths

Solution

4.0 (1 ratings)

33. (2) Let the work be complete in ( x ) days. Then, according to the question, ( frac{x}{16}+frac{x-8}{32}+frac{x-6}{48}=1 ) ( Rightarrow frac{6 x}{96}+frac{3(x-8)}{96}+frac{2(x-6)}{96}=1 ) ( Rightarrow 6 x+3 x-24+2 x-12=96 ) ( Rightarrow quad 11 x-36=96 ) ( Rightarrow quad x=frac{96+36}{11} ) ( therefore quad x=frac{132}{11}=12 ) days