Question

A sum of money is sufficient to pay A′s wages for 21 days and B′s wages for 28 days. The same money is sufficient to pay the wages of both for _______:
A. 12 days
B. $12\dfrac{1}{4}$ days
C. 14 days
D. $24\dfrac{1}{2}$ days.

Answer 1

Hint: First assume the total money amount. Then find the one day wages for each one. Then after compute the one day wage of both taken together. At last find out the number of days for then working together.

Complete step-by-step answer:
Let us assume that the sum of money sufficient to pay is ‘x’.
It is given that this amount is sufficient for A’s wages for 21 days.
So, A’s per day wage = $\dfrac{x}{{21}}$
Also, it is given that this amount is sufficient for B’s wages for 28 days.
So, B’s per day wage = $\dfrac{x}{{28}}$
Now, we compute the per day wage of bother A and B, working together,
= $\dfrac{x}{{21}}$ + $\dfrac{x}{{28}}$
Solving it , we get ,
$ \Rightarrow
  \dfrac{x}{{21}} + \dfrac{x}{{28}} \\
   \Rightarrow \dfrac{{4x + 3x}}{{84}} \\
   \Rightarrow \dfrac{{7x}}{{84}} \\
   \Rightarrow \dfrac{x}{{12}}$
Further,
We compute no. of days needed for A and B to get ‘x’ wage together, as follows:
$
  \dfrac{{Total\;amount}}{{\;one\;day\;wage\;together}} \\
   \Rightarrow \dfrac{x}{{\dfrac{x}{{12}}}} \\
   \Rightarrow 12 \\
 $
$\therefore $ The same money is sufficient to pay the wages of both A and B for 12 days.

So, the correct answer is “Option A”.

Note:In simple arithmetic such problems are very popular. These are to find the relationship between work done, time taken and wage paid. Also, direct and inverse relationships have to be taken care of between the given terms to get the correct expression and hence the result. It is a fact that work done is directly proportional to the time taken.And also work done is directly proportional to the money paid. Here, computation on unit quantity base plays an important role.