Question

A and b can complete a piece of work in 80 days and 120 days respectively. they started working together but a left after 20 days. after another 12 days c joined b and they completed the work in 28 more days. in how many days c can alone complete the work?

Answer 1

32 days..............

Answer 2

Answer:

'c' alone requires 112 days to complete the work.

Step-by-step explanation:

Given : A and b can complete a piece of work in 80 days and 120 days respectively. they started working together but a left after 20 days. after another 12 days c joined b and they completed the work in 28 more days.

To find : In how many days C can alone complete the work?

Solution :

'a' complete work in 80 days.

Work complete by 'a' in 1 day = $\frac{1}{80}$

'b' complete work in 120 days.

Work complete by 'b' in 1 day = $\frac{1}{120}$

According to question,

'a' and 'b' worked in the initial 20 days, then 'b' alone worked alone for 12 days, then 'b' and 'c' worked for 28 days and completed the work.

$(a+b)20 + 12b+ 28(b+c) = 1$

$20a + 20b + 12b + 28b + 28c= 1$

$20a + 60b + 28c= 1$

Substitute the value of a and b,

$20\times \frac{1}{80} + 60\times \frac{1}{120} + 28c = 1$

$\frac{1}{4} +\frac{1}{2} + 28c= 1$

$\frac{3}{4}+ 28c = 1$

$28c=\frac{1}{4}$

$c=\frac{1}{4\times 28}$

$c=\frac{1}{112}$

Therefore, 'c' alone requires 112 days to complete the work.