Question

three person A, B and C working together can dig a pit in 15 days whereas the person A alone can do it in 40 days and B alone can do it in 30 days .at what time will the person C alone can do it?​

Answer 1

Answer:

C alone can complete the work in 120 days

Step-by-step explanation:

Answer 2

Person C alone can do it in 120 days

Solution:

Three person A, B and C working together can dig a pit in 15 days

We know that,

$\text { Efficiency } \times \text { number of days }=\text { total work }$

Therefore,

(Efficiency of A, B and C) × 15 days = total work  …(1)

Person A alone can do work in 40 days

(Efficiency of A) × 40 days = total work     …..(2)

B alone can do work in 30 days

(Efficiency of B) × 30 days = total work      …(3)

From (2) and (3),

$\begin{array}{l}{\frac{(\text { Efficiency of } \mathrm{A}) \times 40 \text { days }}{(\text { Efficiency of } \mathrm{B}) \times 30 \mathrm{days}}=\frac{\text { total work }}{\text { total work }}} \\\\ {\frac{(\text { Efficiency of } \mathrm{A})}{(\text { Efficiency of } \mathrm{B})}=\frac{30}{40}=\frac{3}{4}}\end{array}$

Efficiency of A : Efficiency of B = 3 : 4

Putting Efficiency of A in equation (2) we can get total work

3 × 40 = 120 = Total work                  ….(4)

Now using these values in equation (1), we get

(Efficiency of (A+B+C)) × 15 = 120

(3 + 4 + c) × 15 = 120

(7 + c) = 120 ÷ 15

7 + c = 8

c = 8 – 7 = 1 (which is the efficiency of C)  

Time Taken by C to complete work alone $=\frac{120}{1}=120 \mathrm{days}$

Learn more about time and work

A B and C working together can finish a piece of work in 8 hours a alone can do it in 20 hours and B alone can do it 24 hours in how many hours will see alone do the same work

https://brainly.in/question/1798758

Three workers rahul,sumit and ajay undertook a work a work to dig a pit. When sumit and rahul work together, they take 6 days to dig the pit. However, when rahul and ajay work together, they take 9 days to finish the same task. When rahul worked alone, he took thrice as much time that would be taken by all three working together. How much time is required if they all work on the same task

https://brainly.in/question/7391898