Question

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

Answer 1

Step-by-step explanation:

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}x1 and the one day work of B will be \frac{1}{y}y1 .

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}x1+y1=151    {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}x1=23×y1

                                \frac{1}{x} = \frac{3}{2y}x1=2y3   --------------------- [equation 2]

Putting this value in equation 1 we get;

                                \frac{3}{2y} + \frac{1}{y}= \frac{1}{15}2y3+y1=151

                                   \frac{3+2}{2y} = \frac{1}{15}2y3+2=151

                                 2y = 5 \times 152y=5×15

                                    y=\frac{75}{2}y=275

                                    y = 37.5 days

Now, putting this value in equation 2 we get;

                                     \frac{1}{x} = \frac{3}{2y}x1=2y3

                                     2y = 3\times x2y=3×x

                                     x=\frac{2\times 37.5}{3}x=32×37.5

                                     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:

Solution

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Let

A’s one day work be x and B’s one day work be y.

Then according to the question,

x= 2

3 y

⇒2x=3y

⇒2x−3y=0 … (i)

Also given, in 15 days: A and B together can do a piece of work

So, according to this condition we have

x+y= 15 +1

⇒15(x+y)=1

⇒15x+15y=1 … (ii)

Multiplying equation (i) by 5, we get

10x–15y=0 ... (iii)

Subtracting equation (ii) from (iii), we get

25x=1

⇒x= 25

1

On substituting the value of x in equation (i), we get

2⋅ 25

1

−3y=0

⇒25

2

=3y

⇒y= 75

2

Therefore,

Man A will do the work in

x

1

days = (1/25)

1

=25 days and

Man B will do the work in

y

1

days = (2/75)

1

= 2

75

=37

2

1

days