p and q started a business. they made an annual profit of rs 50000. q being a working partner received 20 % of the annual profit as his salary. if the entire profit were divided in the ratio of their investment, p would received rs 8000 more as his profit share than what he actually got. find p's actual profit share in rs
Please explain easy way
Let the investments of P and Q be `p and `q respectively.
Salary of Q = `10000
(40000) 8000
p q
p
(50000)
p q
p +
+
=
+
p : q = 4 : 1
Profit share of p =
5
4
(40000) = `32000 Ans: (32000)
Let's start by assigning variables to the given information:
Let P be the profit share of partner P.
Let Q be the profit share of partner Q.
Let x be the total profit.
We know that:
P + Q = x (Equation 1)
Q = 0.2x (Q's salary is 20% of the profit) (Equation 2)
If the entire profit were divided in the ratio of their investment, P would have received rs 8000 more. This means that:
P = Q + 8000 (Equation 3)
Now, let's solve the system of equations:
Substitute Equation 2 into Equation 1:
P + 0.2x = x
Rearrange the equation:
P = 0.8x (Equation 4)
Substitute Equation 2 into Equation 3:
0.2x + 8000 = Q + 8000
Simplify the equation:
0.2x = Q
Substitute Equation 2 back into Equation 4:
P = 0.8(0.2x + 8000)
Simplify the equation:
P = 0.16x + 6400
Now, substitute P and Q from Equations 2 and 3 into Equation 1:
0.16x + 6400 + 0.2x = x
Combine like terms:
0.36x + 6400 = x
Move x to the left side of the equation:
0.36x - x = -6400
Combine like terms:
-0.64x = -6400
Divide both sides by -0.64:
x = 10000
Thus, the total profit x is Rs 10,000.
Substitute the value of x into Equation 2 to find Q:
Q = 0.2(10000)
Q = Rs 2000
Substitute the value of Q into Equation 3 to find P:
P = 2000 + 8000
P = Rs 10000
Therefore, partner P's actual profit share is Rs 10,000.
To solve this problem, let's break it down step by step:
Step 1: Calculate q's salary
We know that q received 20% of the annual profit as his salary. So, 20% of rs 50000 can be calculated as (20/100) * 50000 = rs 10000.
Step 2: Find the remaining profit
To find the remaining profit, we need to subtract q's salary from the total annual profit. So, rs 50000 - rs 10000 = rs 40000.
Step 3: Calculate the extra profit that p would receive
According to the problem, if the profit were divided in the ratio of their investments, p would receive rs 8000 more as his profit share. This means that rs 8000 is the difference between what p actually received and what he would have received.
Step 4: Determine the ratio of investments
Let's assume that p invested x amount and q invested y amount. According to the problem, p would have received rs 8000 more if the profit was divided in the ratio of their investments. This can be represented as x - y = rs 8000.
Step 5: Set up a proportional equation
Since the annual profit is divided between p and q in the ratio of their investments, we can set up a proportion using the given information. The equation would be (x - 8000) / (y + 10000) = x / y.
Step 6: Solve the equation to find the values of x and y
Solving the equation (x - 8000) / (y + 10000) = x / y for x and y will give us the values of their investments.
Step 7: Calculate p's actual profit share
Now that we have the values of x and y, we can calculate p's actual profit share. p's profit share can be determined by multiplying the ratio of his investment with the remaining profit, which is rs 40000. So, p's actual profit share is (x / (x + y)) * 40000.
By following these steps, we can find the value of p's actual profit share in rs.