Question

A and B together can do a piece of work in 15 days. If A’s one day work be 3/2 times the one  day’s work of B; find in how many days each alone will do the work. 

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Answer 1

A alone will do the work in 25 days and B alone will do the work in 37.5 days.

Step-by-step explanation:

We are given that A and B together can do a piece of work in 15 days. Also,  A’s one day work be (3/2) times the one day’s work of B.

Let A alone can do the work in 'x days' and B alone can do the work in 'y days'.

This means that the one day work of A will be $\frac{1}{x}$ and the one day work of B will be $\frac{1}{y}$ .

Now, according to the question;

• The first condition states that A and B together can do a piece of work in 15 days, that is;

          $\frac{1}{x} + \frac{1}{y}= \frac{1}{15}$    {in one day they do this much work}  ------ [equation 1]

• The second condition states that A’s one day work be (3/2) times the one day’s work of B, that is;

                                $\frac{1}{x} = \frac{3}{2}\times \frac{1}{y}$

                                $\frac{1}{x} = \frac{3}{2y}$   --------------------- [equation 2]

Putting this value in equation 1 we get;

                                $\frac{3}{2y} + \frac{1}{y}= \frac{1}{15}$

                                   $\frac{3+2}{2y} = \frac{1}{15}$

                                 $2y = 5 \times 15$

                                    $y=\frac{75}{2}$

                                    y = 37.5 days

Now, putting this value in equation 2 we get;

                                     $\frac{1}{x} = \frac{3}{2y}$

                                     $2y = 3\times x$

                                     $x=\frac{2\times 37.5}{3}$

                                     x = 25 days.

Hence, A alone will do the work in 25 days and B alone will do the work in 37.5 days.

Answer 2

Answer:

a and b together do a work in 15 days