Question

Bran takes twice the time than Jon and thrice the
time than Bob to complete a task. Together they
all finish the work in 1 day. What is the time taken
by Bran to complete the work alone?​

Answer 1

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Answer 2

Given:

Bran takes twice the time than Jon and thrice the  time than Bob to complete a task. Together they  all finish the work in 1 day.

To Find:

The time taken  by Bran to complete the work alone.

Solution:

From the given information we can find the ration of time taken by Bran, Jon, and Bob,

The ratio is $= 6:3:2$

So, their efficiency will be in the ratio $= \frac{1}{6}:\frac{1}{3}:\frac{1}{2}$  

                                                              $=1:2:3$

Let,

Unit work done by Bran per day $=x$

Unit work done by Jon per day $=2x$

Unit work done by Bob per day $= 3x$

So,

Work done by all three of them together per day $=x+2x+3x$

                                                                                 $=6x$

So,

Time taken by Bran to do the work $=\frac{Work done by all three of them together per day}{Unit work done by Bran per day}$

                                                           $= \frac{6x}{x}$  

                                                           $=6$

Hence, the time taken by Bran to do the work alone is 6 days.