Question

 A can do a piece of work in 24 days and B in 20 days but with the help of C they finished the work in 8 days. C alone can do the work in how many days?​

Answer 1

hope it will be helpful

Answer 2

GIVEN: A does a piece of work in 24 days; B does the work in 20 days; B with the help of C does the work in 8 days

TO FIND: How much time will C take to complete the same work

SOLUTION:

• For completing the same work A, B, B and C together are taking different days.
• Because the capacity of doing the work differs from person to person.
• As we don't know in how many days C will complete the work so we are assuming that it be x.

C alone will complete the work in days=

$\frac{1}{A}$ + $\frac{1}{B}$ + $\frac{1}{C}$ = $\frac{1}{8}$

$\frac{1}{24}$ + $\frac{1}{20}$ + $\frac{1}{x}$ = $\frac{1}{8}$

$\frac{1}{24}$ + $\frac{1}{20}$ - $\frac{1}{8}$ = -$\frac{1}{x}$

Now we will take the LCM of 24,20,8 as 120.

$\frac{5 + 6 - 15}{120}$ = -$\frac{1}{x}$

$\frac{-4}{120}$ = $\frac{-1}{x}$

Now we will cross multiply

-4 x = -120

x = 30

C will take 30 days to complete the same task.

C will take 30 days to complete the same task.