Since we have been given the work completed by both Jon and Tom along with the respective time that they took, it is good to work out the rate/efficiency of working of Jon and Tom. In general, it is advised to work on finding out the rate/efficiency in most Time & Work problems, since it simplifies problem-solving to a great extent.
Let us assume the following variables:
If Jon can make 'x' chairs per day, then Tom can make '3x' chairs per day. Similarly, if Tom can make 'y' tables per day, then Jon can make '2y' tables per day.
Therefore, working together, Jon and Tom can make '4x' chairs per day and Jon and Tom can make '3y' tables per day.
But as per the problem, they have taken 6 days to complete making the tables and 9 days to complete making the chairs. Hence, their combined efficiency in making tables is 1/6 per day (assuming the work of making 2 tables as 1 unit) and their efficiency in making chairs is 1/9 per day (similar assumption on the work of making 10 chairs as 1 unit).
Hence, we can equate 4x and 1/9 since both represent the efficiency of making chairs; similarly, we can equate 3y and 1/6 since both represent the efficiency of making tables.
4x = 1/9
=> x = 1/36 i.e. Jon can do 1/36 units of work per day. Therefore,
3x = 1/12 i.e. Tom can do 1/12 units of work per day. Hence, he will take 12 days to complete the work, which is nothing but that of making 10 chairs.
Likewise,
3y = 1/6
=> y= 1/18 i.e. Tom can do 1/18 units of work per day. Hence, he will take 18 days to complete the work, which is the work of making 2 tables.
Hence, option (C).
Key points:
It is not necessary to calculate the individual efficiencies for making one chair or one table. It is enough to assume the given work of 2 tables and 10 chairs as 1 unit and then calculate the efficiencies of each person wrt this 1 unit. This will save time and also reduce complex calculations.
It is good to start off by assuming simple variables for the efficiencies, as we did since we will be able to equate the variables to the given data at some stage of the solution.
Hope this helps!
Cheers,
CrackVerbal Academics Team
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