A can do a piece of work in 40 days; b can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. c alone can do the whole work in?
by J Nandhini
Updated Sep 12, 2023
A can do a piece of work in 40 days; b can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. c alone can do the whole work in?
Let's break down the problem step by step:
A can complete the work in 40 days, so in one day, A can complete 1/40th of the work.
B can complete the work in 30 days, so in one day, B can complete 1/30th of the work.
Now, let's calculate how much work A and B completed when they worked individually for 10 days each.
A completed (1/40) * 10 = 1/4th of the work in 10 days.
B completed (1/30) * 10 = 1/3rd of the work in 10 days.
Now, let's find out how much work is left after A and B worked for 10 days each:
1 - (1/4 + 1/3) = 1 - (3/12 + 4/12) = 1 - 7/12 = 5/12 of the work is left.
Now, we know that C finished the remaining 5/12 of the work in 10 days.
To find how much work C can complete in one day, we divide 5/12 by 10:
(5/12) / 10 = 5/120 = 1/24
So, C can complete 1/24th of the work in one day.
To find out how long it would take C to complete the entire work alone, we can take the reciprocal of 1/24, which gives us:
1 / (1/24) = 24
So, C alone can complete the whole work in 24 days.
