Question

A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone?
(a) 7.5 days
(b) 8.5 days
(c) 9.5 days
(d) 11.5 days

Answer 1

Hint: Let M and S represent the man and his son. The work done by man and son in one day is taken as \[\dfrac{1}{M}\] and \[\dfrac{1}{S}\] and total the work done in one day is \[\dfrac{1}{3}\]. Thus sum is together and find the value of \[\dfrac{1}{S}\].

Complete step-by-step answer:
Let us represent the man as ‘M’ and his son as ‘S’. It is said that the man, M can do a piece of work in 5 days. The piece of work can be finished in 3 days if his son helps him.
Work done by M on 1 day = \[\dfrac{1}{5}\].
M and S can finish the work in 3 days.
\[\therefore \] Work done by M and S in 1 day = \[\dfrac{1}{3}\].
i.e. work done by M + work done by S = \[\dfrac{1}{3}\].
\[\Rightarrow \dfrac{1}{M}+\dfrac{1}{S}=\dfrac{1}{3}\]
We know, \[\dfrac{1}{M}=\dfrac{1}{5}\], as the work done by the man in 1 day.
\[\therefore \dfrac{1}{S}=\dfrac{1}{3}-\dfrac{1}{M}=\dfrac{1}{3}-\dfrac{1}{5}=\dfrac{5-3}{15}=\dfrac{2}{15}\]
i.e. \[\dfrac{1}{S}=\dfrac{1}{7.5}\]
\[\therefore S=\dfrac{15}{2}=7.5\]
\[\therefore \] Work done by S in one day = \[\dfrac{1}{7.5}\].
Which means that the son will take 7.5 days to complete the work alone.
So, the correct answer is “Option A”.

Note: The total work by S and M will take 3 days. Thus the equation formed won’t be \[S+M=\dfrac{1}{3}\], which would be wrong. The work done by them in one day will be \[\dfrac{1}{M}\] and \[\dfrac{1}{S}\].