Question
Determine Bhanu's initial investment, given that Aman,
Bhanu, and Chintu started a business together. Statement I: The investment ratio of Aman, Bhanu, and Chintu is 2 : 3 : 4. After 4 months, Aman adds Rs. 10,000 to his investment. After 2 more months, Chintu withdraws Rs. 10,000. The final profit-sharing ratio among Aman, Bhanu, and Chintu is 16 : 18 : 21. Statement II: The investment ratio of Aman, Bhanu, and Chintu is 2 : 3 : 4. After 5 months, Aman increases his investment by Rs. 5,000. After 3 more months, Bhanu withdraws Rs. 10,000. The total profit at the end of the year is Rs. 10,75,000. The questions contain two statements as statement I and statement II. Determine which statement/s is/are necessary to answer the question and give an answer as,Solution
ATQ,
From statement I, The share of Aman, Bhanu and Chintu, = > [2x * 4 + (2x + 10000) * 8] : [3x * 12] : [4x * 6 + (4x – 10000) * 6] = 16 : 18 : 21 = > [8x + 16x + 80000] : [36x] : [24x + 24x – 60000] = 16 : 18 : 21 = > [24x + 80000] : [36x] : [48x – 60000] = 16 : 18 : 21 ATQ, (24x + 80000) / 36x = (16/18) 24x + 80000 = 32x 8x = 80000 x = 10000 The initial investment of Bhanu = 3x = Rs. 30000 Statement I alone is sufficient to answer the question. From statement II, The share of Aman, Bhanu and Chintu, = > [2x * 5 + (2x + 5000) * 7] : [3x * 8 + (3x – 10000) * 4] : [4x * 12] = > [10x + 14x + 35000] : [24x + 12x – 40000] : [48x] = > [24x + 35000] : [36x – 40000] : [48x] Given, 24x + 35000 + 36x – 40000 + 48x = 1075000 108x = 1080000 x = 10000 The initial investment of Bhanu = 3x = Rs. 30000 Statement II alone is sufficient to answer the question. So, either statement I or II is sufficient to answer the given question.
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