Question

A,B and C can do a piece of work in 10 day . A alone can do it in 40 day ,and B alone can do it in 30 day . in how many days will C alone do the same work ?

Answer 1

Okay, so to figure out how much work is being done, we can take the LCM of all 3 numbers, which ends up being 60.

A,B,C can do 60 work in 10 days, which means that they combined work 6 per day

A, B can do 60 work in 10 days, which means they do a combined 5 work per day

A, C can do 60 work in 20 days, which means they do a combined 3 work per day

If A+B is 6, then A+B+C (which we know is 6) minus6=C

Thus, C=6–5=1

C does 1 work per day

If C is 1, then A+C (which we know is 3) minus 1=A

Thus, A=3–1=2

A does 2 work per day (a bit better, but let’s see who does it all)

If A is 2, then A+B (which we know is 5) minus 2=B

Thus, B=5–2=3

B does 3 work per day (wow! the combined work of A and C, this guy does a lot!)

Let’s Check It!

A+B+C gives the work done by all 3 per day, which is 2+3+1=6

Since they all together do 6 work per day, they would finish the 60 work in 10 days.

Okay, so we know how much they do per day, so how long would it take them to do 60 work?

A does 2 work per day, and would have 60 work completed in 60/2=30 days

B does 3 work per day, and would have 60 work completed in 60/3=20 days

C does 1 work per day, and would have 60 work completed in 60/1=60 days

Answer 2

A + B + c= 10
A = 40
B= 30
total work = LCM of 10,30,40= 120
efficiency---
A+B +C = 12
A = 3
B = 4
put the efficiency of ---
3+ 4 + C = 12
c = 12- 7 = 5
C' s complete work = total work/ efficiency of c = 120/5 = 24 days
»»24 days will be the answer