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Vansh and Aman started a business with Rs. 20000 and Rs. 24000 respectively as their capital investment. Shubham joined them after M months and invested Rs. 36 000 and M months before the end of year Aman left the business. If at the end of the year share profit of Vansh, Aman and Shubham is in the ratio of 4 : 2 : 3, what is the value of M.

Vansh and Aman started a business with Rs. 20000 and Rs. 24000 respectively as their capital investment. Shubham joined them after M months and invested Rs. 36 000 and M months before the end of year Aman left the business. If at the end of the year share profit of Vansh, Aman and Shubham is in the ratio of 4 : 2 : 3, what is the value of M. Correct Answer 7 months 

Given

Vansh and Aman invested in business respectively = Rs. 20000 and Rs. 24000

Shubham invested in business = Rs. 36000

Ratio of their Profit = 4 : 2 : 3

Formula used

Investment = capital × time

Calculation 

Ratio of their capital investment = 20000 : 24000 : 36000

⇒ 5 : 6 : 9

According to question

Ratio of time of investment = 12 : 12 – M : 12 – M

Total ratio = 5 × 12: 6 × (12 – M) : 9 × (12 – M)

⇒ 60 : 72 – 6M : 108 – 9M

Ratio of profit of Vansh and Aman

⇒ 60/ (72 – 6M) = 4/2 (Cross Multiplication)

60 = 2 × (72 - 6M)

⇒ M = 7 Months

∴ The value of M is 7 Months.

 Additional Information

Solution verification, assumption M = 7
      
  Vansh Aman Shubham
Investment (in Rs.) 20000 24000 36000
Time duration (in months) 12 5 5
       
Profit 240000 120000 180000
Profit/12000 2 1 1.5
(Profit/6000) 4 2

3

Ratio of their Profit = 4 : 2 : 3

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