Jon is twice as efficient as Tom in making tables and Tom is thrice as

Question

Jon is twice as efficient as Tom in making tables and Tom is thrice as efficient as Jon in making chairs. Tom receives an order to construct 2 tables and 10 chairs. They jointly complete tables in 6 days and chairs in 9 days. Find out how many days will Tom take to individually complete both chair and tables?

A. Tables in 9 days; Chairs in 36 days

B. Tables in 18 days; Chairs in 36 days

C. Tables in 18 days; Chairs in 12 days

D. Tables in 12 days; Chairs in 18 days

E. Tables in 9 days; Chairs in 12 days

Princ · Answer

OA: C

Let  t  be rate of making Table per day i.e.  t \quad \frac{Table}{Day}

Let  c  be rate of making Chair per day i.e.  c \quad \frac{Chair}{Day}

\begin{matrix}
 & Table & Chair \
 Jon's \quad rate & 2t & c \
 Tom's \quad rate & t & 3c \
 Total \quad rate & 3t & 4c
 \end{matrix}

Total Tables produced in  6  days  = 6 \quad Days * 3t \quad \frac{Table}{Day}=2 \quad Tables

18t=2 \quad;\quad t=\frac{1}{9}\quad \frac{Table}{Day}

Tom's rate  = t

Number of days required by Tom to produce  2  Tables  = \frac{2 \quad Tables}{\frac{1}{9}\quad \frac{Table}{Day}} = 18 \quad Days

Total Chairs produced in  9  days  = 9 \quad Days * 4c \quad \frac{Chair}{Day}=10 \quad Chairs

36c=10 \quad;\quad c=\frac{10}{36}\quad \frac{Chair}{Day}

Tom's rate  = 3c

Number of days required by Tom to produce  10  Chairs  = \frac{10 \quad Chairs}{3*\frac{10}{36}\quad \frac{Chair}{Day}} = 12 \quad Days

pushpitkc · Answer

Jon does 2U units of the table for every U unit of the table Tom does. Together, they make 3U units of the table every day.
Jon does U unit of the chair for every 3U units of the chair Tom does. Together, they make 4U units of the chair every day.

2 table in 6 days -> 18 tables in 54 days. Similarly, 10 chairs in 9 days -> 60 chairs in 54 days

Together, they make 3U table in a day which is 54*3U = 162U tables in 54 days
Similarly, they make 4U chair in a day which is 54*4U = 216U chairs in 54 days
 
1 table is  \frac{162U}{18}  units and 1 chair is  \frac{216U}{60}  units respectively

Tom will take  \frac{162U}{18} * \frac{1}{U} = \frac{81}{9} = 9  days to make a chair and  \frac{216U}{60} * \frac{1}{3U} = \frac{54}{45}  days to make a table

Therefore, the order - 2 tables takes  18  days and 10 chairs takes  \frac{54}{45}*10 = 12  days - to make. (Option C)

AkshdeepS · Answer

Let us work on tables first :

Say, Tom's rate = r

Then John's rate = 2r

Total Time = 6 hours

Total work = 2 tables

Tom's work + John's work = Total work

6r + 6*2r = 2

r = 1/9 (Tom's individual rate)

We know work = 2 tables

Therefore Tom's individual time = Work/ Rate = 2/(1/9) = 2*9 = 18 days

Let us work on chairs :

Say,John's rate = r

Then Tom's rate = 3r

Total Time = 9 hours

Total work = 10 chairs

Tom's work + John's work = Total work

9*3r + 9*r = 10

27r + 9r = 10

r = 5/18 (John's individual rate)

3*5/18 = 5/6 (Tom's individual rate)

We know work = 10 chairs

Therefore, Tom's individual time = Work/ Rate = 10/(5/6) =  12 days

Hence (C)

KarishmaB · Answer

Tom's Rate of making tables = T, making chairs = 3C
Jon's rate of making tables = 2T, making chairs = C

Joint rate of making tables = 3T = 2 tables in 6 days = 1/3 table per day
T = 1/9 table per day
Time taken by Tom to make 2 tables = 2/(1/9) = 18 days

Joint rate of making chairs = 4C = 10 chairs in 9 days = 10/9 chairs per day
3C = 30/36 chairs per day
Time taken by Tom to make 10 chairs = 10/(30/36) = 12 days

Answer (C)

laulau · Answer

Chairs: J=2T-> 3 units total
Tables: T=3J-> 4 units total

Tom's rate for assembling chairs =\(\frac{2}{6}*\frac{1}{3}\) \(= \frac{2}{18}\)
# days to assemble to chairs using the work-rate equation=\(\frac{2}{18}\)*18=2

Tom's rate for assembling tables =\(\frac{10}{9}*\frac{3}{4}=\frac{30}{36}\)
# days to assemble 10 tables using the work-rate equation = \(\frac{30}{36}\)*12=10

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CrackverbalGMAT · Answer

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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