Question

A worker is digging a ditch. He gets 2 assistants who work 2/3 as fast as he does. If all 3 worl on a ditch they should finish it in fraction of time that the worker takes working alone? (1) 3/7 ; (2) 1/2 ; (3) 3/4 ; (4) 4/3

Answer 1

Let us consider that ,
The worker can complete the work in x hours .
So, he can complete 1/x part of work in 1 hour.

Now, The workers does 2/3 of what he does. So they do 2/3(1/x) part of work in 1 hour . 2/3x work in 1 hour .

Consider them all working together,
So work done in one hour, = 1/x + 2/3x + 2/3x = 3 + 4 / 3x = 7/3x .

So, They taken 1 hour to complete 7/3th part of work. So, In 3x/7 hours , They all can complete the work.

Ratio of the time taken by all instead of only one = 3x/7 : x = 3/7 .

So ,The required option is ( 1 )

Hope my answer helped you!

Answer 2

time taken by all= X+2x/3+2x/3=7x/3

so,they will complete the work in 3/7 hr