Question

A and B can finish work in 30 days while with the assistance of C they can finish
in 26
2/3
days. How much time will C alone take to finish
a. 120 days
b. 240 days
c. 200 days
d. 150 days

Answer 1

Given,

A and B both finish the work in 30 days.

1 day work of A and B,

$\[ = \frac{1}{{30}}\]$

A, B and C finish the work in $\[26\frac{2}{3}\]$ days or $\[\frac{{80}}{3}days\]$

1 day work of A, B with C,

$\[ = \frac{3}{{80}}\]$

Solution,

Calculate the time taken by C to complete the task alone,

= 1 day work of A, B, and C - 1 day work of A and B

$\[ = \frac{3}{{80}} - \frac{1}{{30}}\]$

$\[ = \frac{{90 - 80}}{{80 \times 30}}\]$

$\[ = \frac{{10}}{{80 \times 30}}\]$

$\[ = \frac{1}{{240}}\]$

So, C will complete the work in 240 days.

Hence the correct option is (b), i.e. 240 days.

Answer 2

Answer:

Option (b)

C alone can complete the work in $240$ days

Step-by-step explanation:

Given

A and B can finish work in $30$ days.

$A+B=\frac{1}{30}$

A, B and C can complete the same work in $26\frac{2}{3}$ days.

$A+B+C=\frac{3}{80}$

Equating them we get

$\frac{1}{30}+C=\frac{3}{80} \\\\C=\frac{3}{80} -\frac{1}{30} \\\\C=\frac{90-80}{80*30} \\\\C=\frac{10}{2400}\\\\C=\frac{1}{240}$

C alone can complete the work in $240$ days.