Question
Amit, Bhanu, and Chintu started a
business where Bhanu invested Rs. 1,500 more and Chintu invested Rs. 200 less than Amit. The task is to determine the amount initially invested by Amit. Statement I: The ratio of the time periods for which Amit, Bhanu, and Chintu invested is 3:4:5, respectively. Also, the combined profit share of Amit and Chintu is equal to 70% of Bhanu's profit share. Statement II: Amit withdrew his investment 6 months after starting the business, while Bhanu and Chintu withdrew their investments 2 months and 4 months after Amit, respectively. If Amit had invested 60% more and Bhanu had invested Rs. 450 less, Chintu's profit share would have remained unchanged. The question consists of two statements numbered "l and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.Solution
ATQ, Let the investment of ‘Amit’ = Rs. ‘y’ Then investment of ‘Bhanu’ = Rs. (y + 1500) Investment of ‘Chintu’ = Rs. (y – 200) Statement I: Ratio of profit shares of ‘Amit’, ‘Bhanu’ and ‘Chintu’, respectively = (y × 3):{(y + 1500) × 4}:{(y – 200) × 5} = (3y):(4y + 6000):(5y – 1000) We have, (3y + 5y – 1000) = (4y + 6000) × 0.7 Or, 8y – 1000 = 2.8y + 4200 Or, 5.2y = 5200 So, y = (5200/5.2) = 1000 So initial investment made by ‘Amit’ = y = Rs 1000 So, data in statement I alone is sufficient to answer the question. Statement II: Time period of investment of ‘Bhanu’ and ‘Chintu’ = (6 + 2) and (6 + 4) i.e. 8 months and 10 months, respectively Increased investment of ‘Amit’ = y × 1.6 = Rs. ‘1.6y’ Decreased investment of ‘Bhanu’ = y + 1500 – 450 = Rs. (y + 1050) According to the statement, (1.6y × 6) + (y + 1050) × 8 = (y × 6) + (y + 1500) × 8 (Since investment and time period of investment of ‘Chintu’ does not change) Or, 9.6y + 8y + 8400 = 6y + 8y + 12000 Or, 17.6y + 8400 = 14y + 12000 So, y = 3600 ÷ 3.6 = 1000
Amit and Sara started a business with the investments of Rs. 20,000 and Rs. 30,000 respectively. After one year, Amit increases his investment by Rs. 5,...
P and Q entered into partnership with Rs. 8000 and Rs. 12000 respectively. After 4 months P withdrew `1/4` of his stock but after 4 months more he put b...
Two firms, X and Y, began a joint venture by investing in a ratio of 9:16. After six months, Firm Y withdrew its entire investment. At the end of the ye...
M and N started a business by investing Rs.4000 and Rs.5000 respectively. After 7 months, M and N increased their investments by 30% and Rs.2400 respect...
‘A’ and ‘B’ invested Rs. 4800 and Rs. 3600, respectively in a business, together. After 6 months, ‘A’ withdrew 25% of his initial investment...
‘A’, ‘B’ and ‘C’ started a business by investing Rs. 3,000, Rs. 3,600 and Rs. 2,400, respectively. After 6 months, ‘B’ decreased his inv...
A, B and C invest in a partnership in the ratio 8:5:10 and investment of A is Rs.200 less than investment of C. Partner B invests for 1/5th and A and C ...
‘A’ invested Rs. 3500 in a business. ‘B’ joined x months later with an investment of Rs. 2500. If at the end of the year, B’s share in the pro...
‘C’ and ‘D’ entered into a business by investing Rs. ‘y’ and Rs. ‘y + 300’, respectively. After 10 months ‘C’ invested Rs. 400 more ...
P and Q started a business by investing Rs.5600 and Rs.4000 respectively. After 6 months, Q increased his investment by a certain percentage such that a...
