Raj invested Rs 76000 in a business. After few months Monty joined him and invests Rs 57000. At the end of the year, both of them share the profits at the ratio of 2:1. After how many months Monty joined Raj?

Raj invested Rs 76000 in a business.

After a few months, Monty joined him and invested Rs 57000.

At the end of the year, both of them share the profits at a ratio of 2:1

We know that the ratio of profits will equal the ratio of investment.

We know Raj invested for 12 months; let us assume Monty invested for N months.

Thus, $$\dfrac{76000\times12}{57000\times N}=\dfrac{2}{1}$$

=> $$\dfrac{4\times12}{3\times N}=\dfrac{2}{1}$$

Thus, N = 8

Therefore, Monty invested for 8 months.

So, Monty invested after 4 months of Raju's investment.