Calculate Total Profit
The problem states that 20% of the total profit is ₹16,800. To find the total profit, we can set up the equation:
\(0.20 \times \text{Total Profit} = ₹16,800\)
Solving for the Total Profit:
\( \text{Total Profit} = \frac{₹16,800}{0.20} = ₹84,000 \)
Determine Investment Ratios
Profit sharing in a partnership is based on the product of investment amount and the duration for which the investment was made. This is often called the "investment-time product".
- Tarun's Investment-Time Product: ₹12,000 × 4 months = ₹48,000
- Varun's Investment-Time Product: ₹72,000 × 10 months = ₹7,20,000
The ratio of their profit shares is the ratio of these products:
\( \text{Ratio of Profit Share (Tarun : Varun)} = ₹48,000 : ₹7,20,000 \)
Simplifying this ratio:
\( \frac{48,000}{7,20,000} = \frac{48}{720} \)
Divide both numerator and denominator by their greatest common divisor, which is 24:
\( \frac{48 \div 24}{720 \div 24} = \frac{2}{30} = \frac{1}{15} \)
So, the profit is shared in the ratio 1 : 15.
Calculate Varun's Profit Share
The total parts in the profit ratio are 1 (Tarun) + 15 (Varun) = 16 parts.
Varun's share is calculated using his ratio part (15) out of the total parts (16) applied to the total profit (₹84,000):
\( \text{Varun's Share} = \left( \frac{15}{16} \right) \times ₹84,000 \)
First, calculate the value of one part:
\( \frac{₹84,000}{16} = ₹5,250 \)
Now, calculate Varun's share:
\( \text{Varun's Share} = 15 \times ₹5,250 = ₹78,750 \)
Therefore, Varun's share of the profit is ₹78,750.
Similar Questions
- A and B start a business by investing ₹40,000 and ₹60,000, respectively. At the end of the year, they earn a profit of ₹20,000. How much profit will A receive?
- Two partners M and N buy a car. M pays his share of $\frac{3}{7}$th of the total cost of the car. M pays ₹ 31,540 less than N. What is the cost of the car?
Important Questions from Partnership
A, B and C invest in a business in the ratio 4 ∶ 5 ∶ 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?
Sumit, Ravi and Puneet invest Rs. 45000, Rs. 81000 and Rs. 90000 respectively to start a business. At the end of the year the total profit is Rs. 4800. 30% of the total profit gives in charity and rest is divided among them. What will be the share of Sumit?
A sum of ₹ 159250 is divided among A, B, C, and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 2 : 5, and that of C and D is 2 : 3. The share (in ₹) of A is:
A and B start a business by investing Rs. 1,00,000 and Rs. 1,50,000 respectively. Find the respective share of each out of a total profit of Rs. 24, 000.
Two partners A and B have started business with the capitals of Rs. 6,000 and Rs. 8,000 respectively. If they made profit of Rs. 5,600 then the share (in Rs.) of A is:
