Question

27 Ravi started a business and Raj joined him after a
few months. The ratio of their investments is 3 : 4.
If their profits at the end of the year are equal, then
find when Raj joined the business?​

Answer 1

Given:

• The ratio of  investment of Ravi and Raj is 3 : 4.

• Their profits at the end of the year are equal.

To Find:

•  When Raj joined the business ?​

Solution:

Let's assume Ravi's investment = 3x

                       Raj's investment = 4x

       Raj invest for T months

      Ravi invest for 12 months

We know that,

             $Profit = Investment \times Time$

Thus,  

              $\frac{Profit_(ravi)}{Profit_(raj)} = \frac{3x \times 12}{4xx \times T}$

            Profit of Ravi = Profit of Raj

So,

               $\frac{Profit_(ravi)}{Profit_(ravi)} = \frac{3x \times 12}{4xx \times T}$

                          $\frac{1}{1} = \frac{3 \times 12}{4 \times T}$

                    $4 \times T = 3 \times 12\\T = 9 months$

Raj invest for 9 months

Raj joined the business $= (12-T)$

                                      $=12-9\\ =3 months$

Thus,  Raj joined after 3 Months from Ravi.

Answer 2

Step-by-step explanation:

Given:

• The ratio of investment of Ravi and Raj is 3 : 4.

• Their profits at the end of the year are equal.

To Find:

• When Raj joined the business?

Solution:

Let's assume Ravi's investment = 3x

Raj's investment = 4x

Raj invest for T months

Ravi invest for 12 months

We know that,

Profit Investment x

Time

Thus,

Profit (ravi) Profit raj) 3x12 4xT

Profit of Ravi = Profit of Raj

Profit(ravi) Profit(ravi) 3x12

3×12

4 × T = 3 × 12

T= 9months

Raj invest for 9 months

Raj joined the business = (12 – T)

= 12 - 9

= 3months

Thus, Raj joined after 3 Months from Ravi.