Question

A can do a piece of work in 12 days and B alone can do it in 16 days. They worked together on it for 3 days and then. A left. how long B take to finish the remaning work?

• A. $8$ days
• B. $5$ days
• C. $7$ days
• D. $9$ days

Answer 1

The correct option is D $9$ days

Alore $A$ can do work in $12$ days. Speed $=x$

Alore $B$ can do work in $16$ days. Speed $=\frac{12x}{16}=\frac{3x}{4}$

If they together work for $3$ days then their speed is $\frac{7x}{4}$]

Work done fraction $=\frac{7x}{4}\times \frac{3}{12x}=\frac{7}{16}$

Remaining work fraction $=\frac{9}{16}$

No. of days $B$ will take to finish total work $=16$ days

No. of days $B$ will take to finish $\frac{9}{16}$ of total work $\frac{9}{16}\times 16$

$=9$ days