Question

Rohit, Lohit and Mohit started a business by investing in the ratio \[\dfrac{1}{3}:\dfrac{2}{4}:\dfrac{2}{5}\]. After \[8\] months Mohit withdrew \[\dfrac{1}{2}\] of his investment. If after \[12\] months from start of business Rohit and Lohit got a share of Rs. \[16,000\] out of the total profit, then find the share of Mohit?

Answer 1

Hint: In his question the ratio of investment by Rohit, Lohit and Mohit \[\dfrac{1}{3}:\dfrac{2}{4}:\dfrac{2}{5}\] respectively but all the investors invest for different time period like Rohit and Lohit invest for \[12\] months but Mohit but different amount for different period of time. So, we will share their profit in terms of their time period.

Compete step by step solution:
As, it is given that the Investment ratio is \[\dfrac{1}{3}:\dfrac{2}{4}:\dfrac{2}{5}\] by Rohit, Lohit and Mohit respectively. After \[8\] months Mohit withdrew \[\dfrac{1}{2}\] of its investment. After \[12\] months from start of business Rohit and Lohit got a share of Rs. \[16,000\] out of the total profit.
Since the ratio of investment is given so we assume that the proportion quantity of the investing ratio be \[x\] . So, the amount of investment ratio will be Rohit : Mohit : Lohit = \[\dfrac{1}{3}:\dfrac{2}{4}:\dfrac{2}{5}\] .
Since, Rohit and Lohit invest for \[12\] months so their profit share will be in the ratio of time period. So, profit will be \[\dfrac{1}{3} \times 12:\dfrac{2}{3} \times 12:\left( {\dfrac{2}{5} \times 8 + \dfrac{1}{5} \times 4} \right)\] .
Since, Mohit withdrew \[\dfrac{1}{2}\] and the remaining amount for next \[4\] months so all the investor profit ratio will be like
\[ = 4x:8x:4x\]
Total profit = \[16x\] .
Total profit of Rohit and Lohit is Rs. \[16,000\] .
\[ \Rightarrow 12x = 16000\]
\[ \Rightarrow x = \dfrac{{16000}}{{12}}\]
On dividing with 4 we get,
\[\therefore x = \dfrac{{4000}}{3}\]
Hence, the share of Mohit = \[4x\]
After substituting the value of x we get,
\[ \Rightarrow 4 \times \dfrac{{4000}}{3}\]
\[ \Rightarrow \dfrac{{16000}}{3}\]
On dividing with 3 we get, \[ \Rightarrow 5,333.33\] Rs.

Note: The question statements are changed at some particular time period of time. So, when a student tries to solve it, be careful about the benefit ratio in terms of time period, otherwise it will lead to the wrong answer.