A began business with Rs. 45000 and B joined afterward with Rs. 30000....
Given:
- A began business with Rs. 45000
- B joined afterward with Rs. 30000
- At the end of a year, the profit is divided in the ratio 2:1
To find:
- When did B join?
Solution:
Let's assume that B joined after x months.
Then, A invested for 12 months and B invested for (12-x) months.
As the profit is divided in the ratio 2:1, we can assume that the total profit earned is 3y (where y is some constant).
Then, A's share of profit = 2y and B's share of profit = y.
We can write the equation for the profit share as follows:
2y = (45000 * 12 / 12) * (12) / (12-x) - (1)
y = (30000 * 12 / 12) * (12-x) / 12 - (2)
Simplifying equation (1), we get:
2y = 45000 * 12 / (12-x)
24y - 2yx = 45000 * 12
Simplifying equation (2), we get:
y = 30000(12-x)/12
12y - yx = 30000(12-x)
Substituting the value of y from equation (2) in equation (1), we get:
24y - 2yx = 45000 * 12
24[30000(12-x)/12] - 2yx = 45000 * 12
720000 - 48x - 2yx = 540000
2yx = 180000 - 48x
yx = 90000 - 24x
Substituting the value of y in equation (2), we get:
12y - yx = 30000(12-x)
12[30000(12-x)/12] - yx = 30000(12-x)
360000 - 12x - yx = 360000 - 30000x
yx - 12x = 30000x
yx = 30000x + 12x
yx = 120x
Equating the value of yx from both equations, we get:
120x = 90000 - 24x
144x = 90000
x = 625
Therefore, B joined after x = 625/5 = 125 months, which is equal to 10 years and 5 months.
Option (a) is correct - B joined after 3 months.
A began business with Rs. 45000 and B joined afterward with Rs. 30000....
Let B invested money for (12-x) months , here x is the months after which B joined.
45000*12/30000*(12-x)=2/1
45*12/30(12-x)=2/1
45*12 = 2*30(12-x)
540=720-60x
60x=720-540
x=180/60
x=3
So B joined after 3 months.