Question

A and B can together complete a piece of work in $10$ days and B and C in $20$ days. A works at it for $4$ days, B for $6$ days and C later completes it in $22$ days. The time taken by C alone to do the work is ?

• A. $20$ days
• B. $30$ days
• C. $40$ days
• D. $50$ days

Answer 1

Answer: (C)

$40$ days

According To Given Information

$\Rightarrow$ $\frac{W}{A}+\frac{W}{B}=\frac{W}{10}$

$\Rightarrow$ $\frac{1}{A}+\frac{1}{B}=\frac{1}{10}$....................................................(1)

$\Rightarrow$$\frac{W}{B}+\frac{W}{C}=\frac{W}{20}$

$\Rightarrow$$\frac{1}{B}+\frac{1}{C}=\frac{1}{20}$...................................................(2)

Subtracting the Above Two Equations we get

$\Rightarrow$$\frac{1}{A}-\frac{1}{C}=\frac{1}{20}$

$\Rightarrow$$\frac{1}{A}=\frac{1}{C}+\frac{1}{20}$

Now,

$\Rightarrow$$4(\frac{1}{A})+6(\frac{1}{B})+22(\frac{1}{C})=1$

using Eq (1 ) and Eq (2)

$\Rightarrow$$4(\frac{1}{C}+\frac{1}{20})+6(\frac{1}{20}-\frac{1}{C})+22(\frac{1}{C})=1$

$\Rightarrow$$C=40$