X, Y, Z enter into a partnership venture with a capital of Rs.1,20,000, in which the contribution of Y and Z are respectively, 40% more and Rs. 1,000 more than that of X. The profit earned is 20% of the capital. Out of this profit, 10% goes towards some incidental expenses. What is the share (in Rs.) of X out of it?
A) 7,500
B) 4,800
C) 7,000
D) 6,300
To find the share of X in the profit, we need to determine the individual contributions of X, Y, and Z.
Let's start by finding the contribution of X. Let's assume X's contribution is 'x'.
According to the given information, Y's contribution is 40% more than X's contribution, which means Y's contribution is x + 0.40x = 1.40x.
Similarly, Z's contribution is Rs. 1000 more than X's, so Z's contribution is x + 1000.
Now, the total capital invested is Rs. 1,20,000. Therefore, the equation becomes:
x + 1.40x + (x + 1000) = 1,20,000
Simplifying the equation:
3.40x + 1000 = 1,20,000
3.40x = 1,20,000 - 1000
3.40x = 1,19,000
Dividing both sides by 3.40 to find the value of x:
x = 1,19,000 / 3.40
x ≈ 35,000
So, X's contribution is approximately Rs. 35,000.
Next, we need to calculate the profit earned. The profit is 20% of the capital, which is:
Profit = 20% of 1,20,000
Profit = (20/100) * 1,20,000
Profit = 24,000
Out of this profit, 10% goes towards incidental expenses:
Incidental expenses = 10% of profit
Incidental expenses = (10/100) * 24,000
Incidental expenses = 2,400
The remaining profit after deducting the incidental expenses is:
Remaining profit = Profit - Incidental expenses
Remaining profit = 24,000 - 2,400
Remaining profit = 21,600
Finally, let's calculate X's share of the profit:
X's share = (X's contribution / Total contribution) * Remaining profit
X's share = (35,000 / (35,000 + 1.40*35,000 + 35,000 + 1000)) * 21,600
X's share = (35,000 / (35,000 + 49,000 + 35,000 + 1000)) * 21,600
X's share = (35,000 / 1,20,000) * 21,600
X's share = (7/24) * 21,600
X's share ≈ 6,300
Therefore, X's share of the profit is approximately Rs. 6,300.
Hence, the answer is D) 6,300.
Let's start by finding out the individual contributions of X, Y, and Z.
Let the contribution of X be Rs. A.
Since the contribution of Y is 40% more than X's, the contribution of Y can be expressed as A + (40/100)A = A + 0.4A = 1.4A.
And since the contribution of Z is Rs. 1,000 more than X's, the contribution of Z can be expressed as A + 1,000.
The total capital of the venture is given as Rs. 1,20,000. So, we can write the equation as:
A + 1.4A + (A + 1,000) = 1,20,000
Combining like terms, we get:
3.4A + 1,000 = 1,20,000
Subtracting 1,000 from both sides, we have:
3.4A = 1,19,000
Dividing both sides by 3.4, we find:
A = 35,000
So, the contribution of X is Rs. 35,000.
Next, let's calculate the profit earned by the venture.
The profit earned is stated to be 20% of the capital, which is given as Rs. 1,20,000. So, the profit is:
(20/100) * 1,20,000 = 24,000
Out of this profit, 10% goes towards incidental expenses. Therefore, the amount remaining is:
24,000 - (10/100) * 24,000 = 24,000 - 2,400 = 21,600
Now, let's calculate the share of X out of this remaining profit.
Since X's contribution is Rs. 35,000, which is a fraction of the total capital of Rs. 1,20,000, we can find X's share of the remaining profit by multiplying X's contribution by the ratio of the remaining profit to the total capital.
X's share of the remaining profit = 35,000 * (21,600 / 1,20,000)
Simplifying this expression, we have:
X's share of the remaining profit = 35,000 * 0.18
X's share of the remaining profit = Rs. 6,300
Therefore, the share of X is Rs. 6,300.
Hence, the correct answer is option D) 6,300.
x+y+z = 120000
y = 1.40x
z = x+1000
solve for x,y,z
profit p = 0.20*120000 = 24000
distribution = 0.90*24000 = 21600
so X's share is x/120000 * 21600