Ram started a business with an investment of ₹ 70,000 . After a few months, Sham joined him with ₹ 60,000 . At the end of the year, the profits were in the ratio of 2:1. After how many months did Sham join ?

Correct option is A

Given:
Ram's investment = ₹70000 for 12 months
Sham's investment = ₹60000 for t months
Profit ratio = 2:1
Formula Used:
Ratio of Profits = Ratio of (Investment × Time)
Solution:
Let Sham's investment period be t months.
Profit Ratio = $$\frac{Ram's\ Investment × Ram's\ Time}{Sham's\ Investment × Sham's\ Time}$$​​
​$$\frac{70000 × 12}{60000 × t} = \frac{2}{1}$$​​

​$$\frac{7 × 12}{6 × t} = 2$$​​

​$$\frac{84}{6t} = 2$$​​

​$$\frac{14}{t} = 2$$​​
t = 7 months
Sham invested his money for 7 months.
Therefore, he joined after (12 - 7) = 5 months.
Final Answer
So the correct answer is (a)