Question

A has started a business with Rs.21,000 and is joined afterwards by B with Rs.36,000. After how many months did B join if the profit at the end of the year is divided equally?
A. 3
B. 4
C. 5
D. 6

Answer 1

Hint: In this problem, we need to find the ratio of the product of the capital invested and time of A and B. then, equate the ratio with 1.

Complete step by step solution:
The capital invested by A is Rs. 21,000.
The capital invested by B is Rs. 36,000.
Use the below mentioned formula.
\[\dfrac{{{C_A} \times {T_A}}}{{{C_B} \times {T_B}}} = \dfrac{{{P_A}}}{{{P_B}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......\left( 1 \right)\]
Where, C is capital, T is time and P is profit.
Substitute, 21,000 for \[{C_A}\], 36,000 for \[{C_B}\], 12 for \[{T_A}\], 1 for \[{P_A}\] and 1 for \[{P_B}\] in equation (1) to obtain the value of \[{T_B}\].
\[
  \,\,\,\,\,\dfrac{{21,000 \times 12}}{{36,000 \times {T_B}}} = \dfrac{1}{1} \\
   \Rightarrow {T_B} = \dfrac{{21 \times 12}}{{36}} \\
   \Rightarrow {T_B} = 7 \\
\]

So, B joins the business after \[12 - 7 = 5\,\,{\text{months}}\] to share equal profit, hence, option (C) is the correct answer.

Note: B should invest more than A in order to share equal profit. If the selling price of an object is greater than the cost price, it causes profit, whereas, if the selling price of object is less than the cost price of the object it causes loss.