'Arman' and 'Malik' initiated a business venture with their individual investments. 'Arman,' who actively participated in the business, received Rs. 2,400 as a commission from the total profit. The remaining profit was divided in proportion to their respective investments. 'Arman' also received 75% of this remaining amount as his profit share. Additionally, 'Malik' received a profit share for his investment that was Rs. 4,000 less than 'Arman's profit share for his investment. Calculate the total profit generated by the business.
We can say that, Let the total profit received from the business be Rs.(4a + 2400) Amount taken by 'Arman' for managing the business = Rs.2,400 So, remaining amount = 4a + 2400 - 2400 = Rs.'4a' Amount received by 'Arman' as his profit share (for his investment) = (0.75 × 4a) = Rs.'3a' Profit share received by 'Malik' = 4a - 3a = Rs.'a' ATQ; 3a - a = 4000 Or, 2a = 4000 Or, a = 2000 So, total profit earned by the business = 4a + 2400 = 4 × 2000 + 2400 = Rs. 10,400
'Anoop' and 'Soni' have investments in the ratio of 8:5, respectively. 'Anoop' invested his amount for 16 years at a simple interest rate of 15% per annum, while 'Soni' invested his sum for 2 years at a compound interest rate of 40% per annum, compounded annually. If the difference between the total amounts received by them is Rs.4,350, determine the difference between the sums they invested.
ATQ, Let the sum invested by 'Anoop' and 'Soni' be Rs. '8a' and Rs. '5a', respectively Amount received by 'Anoop' = (8a × 0.15 × 16) + 8a = 19.2a + 8a = Rs. '27.2a' Amount received by 'Soni' = 5a × {1 + (40/100)}² = Rs. '9.8a' According to the question, 27.2a - 9.8a = 4350 Or, 17.4a = 4350 Or, (4350/17.4) = 250 Required difference = 8a - 5a = 3a = 3 × 250 = Rs. 750
'Amit' and 'Bikash' embarked on a business venture with initial investments of Rs. 20,000 and Rs. 25,000, respectively. After 3 months, 'Chims' entered the partnership by investing Rs. 15,000. In the same period, 'Amit' decided to increase his investment by 20%, while 'Bikash' opted to withdraw 20% of his initial investment. 'Amit' assumed the role of managing partner and was entitled to 40% of the total annual profit generated by the business. The remaining profit was distributed among the partners based on the ratio of their effective investments. Calculate the exact amount received by 'Amit' at the end of the year, given that the total profit amounted to Rs. 37,000.
ATQ, Ratio of profit share of 'Amit', 'Bikash' and 'Chims', at the end of the year = [20,000 × 3 + 24,000 × 9]:[25,000 × 3 + 20,000 × 9]:[15,000 × 9] = 92:85:45 'Amit' gets 40% of the share for managing the business = Rs. 40% of 37,000 = Rs. 14,800 Remaining profit = Rs.37,000 - 14800 = Rs.22,200 The remaining profit is to be distributed among 'Amit', 'Bikash' and 'Chims' based on ratio of their investment, which is 92:85:45 Profit share of 'A' = Rs.(92/222) × 22,200 = Rs.9,200 Total amount received 'Amit' = Rs. 14,800 + 9,200 = Rs.24,000
Armaan, Malik, and Chinky collectively invested Rs. 1.05 lakh in a business. The investment ratios among them are such that Armaan's investment to Malik's is in a 7:3 ratio, and Malik's investment to Chinky's is in a 2:5 ratio. After 9 months, Armaan increased his investment by Rs. 8,000, and Chinky withdrew Rs. 5,000 from her investment. At the end of the year, the total profit from the business amounted to Rs. 84,600. What is Malik's share of the profit?
ATQ, Let amount invested by 'Armaan' and 'Malik' be Rs. '7a' and Rs. '3a', respectively So, amount invested by 'Chinky' = (5/2) × 3a = Rs. '7.5a' 7a + 3a + 7.5a = 1,05,000 Or, 17.5a = 1,05,000 a = 6,000 So, investment by 'Armaan' = 7a = 14 × 6,000 = Rs.42,000 Similarly, Investment by 'Malik' = Rs. 18,000 Investment by 'Chinky' = Rs. 45,000 Ratio of profit share of 'Armaan', 'Malik' and 'Chinky' at the end of the year = [(42,000 × 9) + (50,000 × 3)] : [18,000 × 12] : [(45,000 × 9) + (40,000 × 3)] = 176:72:175 So, profit share of 'Malik' = {72/(176 + 72 + 176)} × 84600 = Rs.14,400
Puneet and Malik began a business venture, initially investing their capital in a 4:5 ratio, respectively. After half a year, Puneet decided to withdraw Rs. 5000 from his investment, and Malik followed suit, withdrawing Rs. 5000 from his own investment. The distribution of annual profits between Puneet and Malik is in a 3:5 ratio. Can you determine the total initial investment made by Puneet and Malik in the business?
We can say that let the amounts invested by Puneet and Malik be Rs. 4p and 5p respectively. According to question, (4p × 6 + (4p – 5000) × 6)/(5p × 6 + (5p – 5000) × 6) = 3/5 (8p – 5000)/(10p – 5000) = 3/5 40p – 25000 = 30p – 15000 10p = 10000 p = 1000 Desired amount = 9 × 1000 = Rs.9,000
Determine the initial investment made by 'Adam' if both 'Adam' and 'Zampa' jointly invested Rs. 7000 in a startup business. After 7 months, 'Adam' added 20% more to his initial investment, and 'Zampa' withdrew 40% of his initial investment. At the end of one year, 'Zampa's profit share out of the total profit of Rs. 4712 is Rs. 3100.
We can say that initial investment made by Adam is Rs.'a' Initial investment made by Zampa is Rs. (7000 – a) Ratio of profit share of Adam to Zampa = (a × 7 + 1.2a × 5):[(7000 – a) × 7 + 0.6 × (7000 – a) × 5] = 13a:(70000 – 10a) According to question; [13a/(70000 – 10a)] = (1612/3100) = 13/25 325a = 910000 – 130a 455a = 910000 a = 2000 Initial investment made by Adam = Rs.2000
'Aditi' and 'Misti' embarked on a business venture, initially investing sums denoted as 'm' and 'm + 3000', respectively. Four months later, 'Aditi' chose to amplify her investment by an additional Rs. 3,000, whereas 'Misti' opted to withdraw Rs. 2,000 from his initial capital. As the year concluded, 'Aditi' claimed her share of the profit, amounting to Rs. 42,000, out of a total profit pool of Rs. 83,000. Could you ascertain the initial capital 'Misti' invested in this enterprise?
ATQ, Ratio of profit shares of ‘Aditi’ and ‘Misti’ = {(4 × m) + 8 × (m + 3000)}:{4 × (m + 3000) + 8 × (m + 3000 – 2000)} = 3(m + 2000):(3m + 5000) Profit share of ‘Misti’ = 83000 – 42000 = Rs. 41,000 ATQ; {3 × (m + 2000)}/{3m + 5000} = (42000/41000) 41 × (m + 2000) = 14 × (3m + 5000) Or, 41m + 82000 = 42m + 70000 Or, m = 12000 So, investment made by ‘Misti’ initially = 12000 + 3000 = Rs.15,000
V and N ventured into a business, investing their capitals in the ratio of 5:7, respectively. The combined investment of V and N amounts to Rs. 2,880. After 5 months, V increased his investment by 25%, while N withdrew one-third of his initial investment. Determine the ratio of the annual profit share of N to V.
ATQ, Initial investment made by V = 2880 × (5/12) = Rs.1,200 Initial investment made by N = 2880 × (7/12) = Rs.1,680 Profits sharing ratio of V and N = {1680 × 5 + 1680 × (2/3) × 7}:{1200 × 5 + 1200 × 1.25 × 7} = 16240:16500 = 812:825
A&B started a business together with a total investment of Rupees 24,000 such that investment made by B rupees 8000 less than that by A. After four months, A reduced his investment to half while B doubled his investment and C joined by making an investment of rupees 12,000. If the difference between the profit received by A&C at the end of year is Rupees 4200, then find the total annual profit received by all of them together.
Let the initial investment made by A be rupees X.\ Therefore, initial investment made by B = x-8000 Or x+x-8000=24000 2x=32000 x= 16000 Therefore, initially investment made by A&B is rupees 16,000 and rupees 8000 respectively. Ratio of profit received by A, B and C = {(16,000 * 4)+(8000 * 8.)}: {(8000*4)+(16,000 * 8.)}:(12,000 * 8) = 4:5:3 Required profit received = 4200*{(4+5+3)/(4-3)} = Rs. 50,400
