Question

A is thrice as efficient as B and B is twice as efficient as C. if A, B and C work together , how long will they take to complete a job which B complete in $10$ days ?

• A. $\frac{20}{9}$ days
• B. $\frac{11}{9}$ days
• C. $3$ days
• D. None of these

Answer 1

The correct option is A $\frac{20}{9}$ days

Work efficiency ratio

$A:B=3:1\times 2$

$B:C=2:1$

$A:B=6:2$

$B:C=2:1$

$A:B:C=6:2:1$

Time ratio

$A:B:C=1:2:6$

$1$ works is done by $B$ in $10$ days.

$2$ works is done by $B$ in $10$ days.

Sum of ratio=$1+2+6=9$

$\therefore 1$ work is done by $A,B$ and $C$=$\frac{20}{9}$days.