A started a business with rs 20000 after 3 months B joined him with rs 40000 after some more months c joined them with rs 100000 B received rs 18000 out of the total annual profit of rs 55000 how many months after A started the business did c join
How to do easy way please help
If C was in the business for x months, then the weighted investment is
(20000*12 + 40000*9 + 100000x) * x/12 = 55000
x ≈ 1, so C joined after about 11 months
To solve this problem, let's break it down step by step:
Step 1: Calculate the total investment at the time B joined.
- A started with Rs 20,000.
- B joined with Rs 40,000 after 3 months.
So, the total investment at the time B joined would be 20,000 + 40,000 = 60,000 Rs.
Step 2: Calculate the remaining investment at the time C joined.
- C joined with Rs 100,000.
- B had received Rs 18,000 out of the total annual profit of Rs 55,000.
So, the remaining profit to be distributed among A, B, and C would be 55,000 - 18,000 = 37,000 Rs.
Step 3: Calculate the share of A and B.
- The total investment at the time B joined was Rs 60,000.
- A's initial investment was Rs 20,000, so his share would be (20,000 / 60,000) * 37,000 = 12,333.33 Rs.
- B's initial investment was Rs 40,000, so his share would be (40,000 / 60,000) * 37,000 = 24,666.67 Rs.
Step 4: Determine the number of months A started the business before C joined.
- Let's assume A started the business x months ago.
- C's investment was Rs 100,000.
- C's share would be (100,000 / 60,000) * 37,000 = 61,666.67 Rs.
Now, we need to find out for how many months A started the business before C joined to get C's share as 61,666.67 Rs.
Since we know A's share (from step 3), we can set up the following equation:
A's share = C's share
12,333.33 Rs = 61,666.67 Rs
(20,000 / (20,000 + B's investment)) * 37,000 = (100,000 / (20,000 + B's investment)) * 37,000
Simplifying this equation:
20,000 = 100,000 / (20,000 + B's investment)
20,000 * (20,000 + B's investment) = 100,000
400,000 + 20,000B = 100,000
20,000B = 600,000
B = 600,000 / 20,000
B = 30
Therefore, B joined 30 months after A started the business.