Question

a and b can do a piece of work in 20 days , b and c can do it in 10 days and c and a can do it in 12 days. how long will they take to do it together and each separately​

Answer 1

Step-by-step explanation:

Always go with the LCM method, as answer can be calculated while the first reading of the question as the calculation involves integers instead of fractions and they are easily handled.

LCM(12,15,20)=60

Now this 60 units can be treated as the total work and we will now calculate the one day work

One day work of A and B = 60/12 = 5 units

One day work of B and C = 60/15 = 4 units

One day work of C and A = 60/20= 3 units

Now if we add all three we get:-

2(A+B+C)=12 units

So one day work of A, B and C put together is 12/2 = 6 units

To find one day work of A:-

One day work of A, B and C together minus one day work of B and C, that is 6–4=2 units

If the total work is of 60 units and the one day work of A is 2 unit, then alone A needs 60/2 = 30 days to finish the work.

The same way we can find the number of days required by B and C to finish the work by themselves.

Believe me, every question on time and work can be solved with this method and it's really a time saver in exams and involves less calculation.