
A can do work in 15 days and B can do the same work in 20 days. If A and B have done work for 4 days together, the fraction of work left?
Answer
512.7k+ views
Hint – The number of days on which the work can be completed by A and B separately is given to us. Now A and B have worked together for 4 days and we need to find the fraction of work which is left. SO let the total work to be done by A and B be P. Using the unitary methods calculate the work done by A and B by per day and using this calculate the work done by them together in 4 days.
“Complete step-by-step answer:”
It is given that A can do a work in 15 days and B can do a work in 20 days.
If A and B have done work for 4 days together then we have to find out the fraction of work left.
Let the total work be P.
So, the work done by A per day is the ratio of total work divided by the number of days in which A can do the work.
So, the work done by A per day $ = \dfrac{P}{{15}}$.
Similarly, the work done by B per day $ = \dfrac{P}{{20}}$.
Now the work done by A and B in four days is
$ \Rightarrow \left( {\dfrac{P}{{15}} + \dfrac{P}{{20}}} \right) \times 4$
Now simplify this we have
$ \Rightarrow \left( {\dfrac{P}{{15}} + \dfrac{P}{{20}}} \right) \times 4 = \dfrac{{28}}{{60}}P$
So, the work left is total work minus the work done by A and B in four days.
So, work left $ = P - \dfrac{{28}}{{60}}P = \dfrac{{32}}{{60}}P = \dfrac{8}{{15}}P$
So, the fraction of work left is $\dfrac{8}{{15}}$.
So, this is the required answer.
Note – Whenever we face such types of problems the key concept here is to simply apply a unitary method to calculate the work done by the individuals per day then use the conditions and information given in the question to get the required entity.
“Complete step-by-step answer:”
It is given that A can do a work in 15 days and B can do a work in 20 days.
If A and B have done work for 4 days together then we have to find out the fraction of work left.
Let the total work be P.
So, the work done by A per day is the ratio of total work divided by the number of days in which A can do the work.
So, the work done by A per day $ = \dfrac{P}{{15}}$.
Similarly, the work done by B per day $ = \dfrac{P}{{20}}$.
Now the work done by A and B in four days is
$ \Rightarrow \left( {\dfrac{P}{{15}} + \dfrac{P}{{20}}} \right) \times 4$
Now simplify this we have
$ \Rightarrow \left( {\dfrac{P}{{15}} + \dfrac{P}{{20}}} \right) \times 4 = \dfrac{{28}}{{60}}P$
So, the work left is total work minus the work done by A and B in four days.
So, work left $ = P - \dfrac{{28}}{{60}}P = \dfrac{{32}}{{60}}P = \dfrac{8}{{15}}P$
So, the fraction of work left is $\dfrac{8}{{15}}$.
So, this is the required answer.
Note – Whenever we face such types of problems the key concept here is to simply apply a unitary method to calculate the work done by the individuals per day then use the conditions and information given in the question to get the required entity.
Recently Updated Pages
Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Statement I Reactivity of aluminium decreases when class 11 chemistry CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

How many valence electrons does nitrogen have class 11 chemistry CBSE
