 QUESTION

# A carpenter made 5 similar tables in 12h 30min 15sec. How long did it take him to make 1 table?

Hint: Divide the given time in the problem by the given number of tables to get the answer. Use the conversion of time from one unit to another with the help of the relations :-
1 minute $=60\operatorname{s}econds$ $\Rightarrow \operatorname{s}econds=\dfrac{1}{60}$ minute
1 hour $=60$ minutes $\Rightarrow$ 1 minute $=\dfrac{1}{60}hour$

Here, it is given that the carpenter made 5 similar tables in 12 hour 30 minutes 15 second and hence, we need to determine the time taken for making only one table by the same carpenter.
So, first of all, we need to convert the given time to only one unit. Hence, let us convert the time given 12 hour 30 minutes 15 seconds to seconds only.
So, as we know there are 60 minutes in one hour and 60 seconds in one 1 minutes. So, we can convert the 12 hours to minutes by using the relation that there are 60 minutes in one hour. So, we get
1 hour $=60$ minutes
12 hour $=60\times 12$ minutes
12 hour $=720$ minutes
It means, now, we have time as 720 minutes + 30 minutes and 15 seconds or 750 minutes 15 seconds.
Now, we can convert 750 minutes to seconds by using the relation between minutes and seconds. As, we know
1 minute $=60$ minutes
So, 750 minutes $=60\times 750=45000$ seconds
It means the time given in the question can be written as 45000 seconds + 15 seconds or 45015 seconds.
So, we get that the carpenter is making 5 tables in 45015 seconds. It means carpenter can make one table in $\dfrac{45015}{5}$ seconds with the help of unitary method; where we know that unitary method is a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value. As here, we need to find for the single unit only (with respect to ‘1’), So, we need not to multiply by any number.
Here, time taken for making one table is $=$ Time taken for 1 table $=\dfrac{45015}{5}$ seconds
Now, divide the numerator and denominator by 5 to get the simplified form of the above fraction. Hence, we get
Time taken for 1 table $=\dfrac{9003}{1}=9003$ seconds
Now, we can convert the time 9003 seconds in minutes by the relation given as
1 minute $=60$ seconds
$\dfrac{1}{60}$ minutes $=1$ second
$\Rightarrow$ 1 second $=\dfrac{1}{60}$ minutes
9003 seconds $=\dfrac{9003}{60}=\dfrac{3001}{20}$
Now, we can divide 3001 by 20 and get the quotient and remainder as 150 and 1 respectively. So, we can write the given fraction as
$\dfrac{3001}{20}=\left( 150+\dfrac{1}{20} \right)$ minutes
Hence, we can not convert $\dfrac{1}{20}$ minutes to seconds by multiplying it by 60 as we have 60 seconds in one minute. So, we get time as
Time $=150$ minutes and $\dfrac{1}{20}\times 60$ seconds
$\Rightarrow$ time $=150$ minutes and 3 second
Now, we can convert 150 minutes to hour by dividing it by 60. So, we get
Time $=\dfrac{150}{60}$ hours and 3 seconds
Time $=\dfrac{5}{2}$ hours and 3 seconds
Now, we can divide ‘5’ by ‘2’ and get quotient and remainder as 2 and 1 respectively; so, we get time as
Time $=\left( 2+\dfrac{1}{2} \right)$ hours and 3 seconds
Time $=2$ hours $+\dfrac{1}{2}$ hours and 3 seconds
Now, we can convert $\dfrac{1}{2}$ hours to minutes by multiplying it by 60 as there are 60 minutes in one hour. So, we get
Time $=2$ hours $+\dfrac{1}{2}\times 60$ minutes and 3 seconds
Time $=$ 2 hours 30 minutes 3 seconds
Hence, time taken to make one table will be 2 hours 30 minutes 3 seconds.

Note: One may convert the given time in an hour as well by dividing the minutes by 60 and seconds by $60\times 60$. And hence get the same answer as well. So, it can be another approach for the question.
Don’t confuse it with the unitary method, it is used for calculating the questions like Ex: If the price of 4 coffee is 10 Rs then what is the price of 6 coffee ?
So, here we need to find the price of 1 coffee and multiply it by 6. So, this simple approach is termed as a unitary method. Don’t confuse this term.
Take care while converting the given time from one form of units to another.