Question

A can do a piece of work in 12 days and B can do the same work in 15 days and A,B and C and together they can finish the work in 5 days. In how many days will C alone complete the work?

Answer 1

Given:

Work(A) = 12 days

Work(B)= 15 days

Work(A, B, C) = 5 days

To Find:

Work(C)

Solution:

One day work of A = $\frac{1}{12}$

One day work of B = $\frac{1}{15}$

One day work for A and B = $\frac{1}{12}$+$\frac{1}{15}$ = $\frac{3}{20}$

One day work of A, B, and C = $\frac{1}{5}$

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

One day work of C= $\frac{1}{5}$ - $\frac{3}{20}$

One day work of C= $\frac{1}{20}$

Hence, Work(C)= 20

C will take 20 days to complete the work alone.

Answer 2

According to the question it is given that,

Work done by A in 12 days,

Work done by B in 15 days,

Work done by A, B, and C in 5 days,

As we have to find that how many days are required for C for completing his work alone.

A (1 day's work) = $\frac{1}{12}$

B (1 day's work) = $\frac{1}{15}$

A and B (1 day's work)

$=>\frac{1}{12}+\frac{1}{15}$

$=>\frac{3}{20}$

A, B, and C (1 day's work) = $\frac{1}{5}$

For C ( 1 day's work alone) = A, B, and C (1 day's work) - A and B (1 day's work)

$=>\frac{1}{5} -\frac{3}{20}$

$=>\frac{1}{20}$

Hence, C can complete the whole work in 20 days.