Three workers A, B and C complete a given piece of work within different time spans while working individually. What is the ratio of efficiencies of C and B respectively? I. A takes 100% more time than C to complete the given piece of work. II. B completes the given piece of work within 8 days. III. B takes 2 days less than A to complete the given piece of work.

Question

Accepted Answer

Step 1: Let A, B, C take $a,b,c$ days respectively. Efficiencies are proportional to reciprocals of times, so ratio of efficiencies of C and B is $\frac{1/c}{1/b}=\frac{b}{c}$.

Step 2 (interpret statements):
- I: "A takes 100% more time than C" gives $a=2c$. 
- II: "B completes the work within 8 days" gives $b=8$. 
- III: "B takes 2 days less than A" gives $b=a-2$.

Step 3 (combine all three): Substitute $a=2c$ from I into III: $b=2c-2$. Using II ($b=8$) we get $8=2c-2\Rightarrow 2c=10\Rightarrow c=5$.

Step 4 (compute ratio): The ratio of efficiencies C:B is $\dfrac{b}{c}=\dfrac{8}{5}$.

Thus using all three statements uniquely determines the ratio as $8:5$, so all three statements together are sufficient.

FINAL_ANSWER: b

Answer

Answer

Answer

Answer