Question:
'A' and 'B' started a business by investing Rs. '10x' and Rs. '20x', respectively. Six months later, 'B' increased his investment by 25%. After 6 more months, 'A' doubled his investment and 'C' joined the business by investing Rs. 5,000. If at the end of two years, the profit share of 'A' was Rs. 2,400 out of total profit of Rs. 10,200, then find the initial investment of 'B'.
'A' and 'B' started a business by investing Rs. '10x' and Rs. '20x', respectively. Six months later, 'B' increased his investment by 25%. After 6 more months, 'A' doubled his investment and 'C' joined the business by investing Rs. 5,000. If at the end of two years, the profit share of 'A' was Rs. 2,400 out of total profit of Rs. 10,200, then find the initial investment of 'B'.
Updated On: Aug 21, 2024
- Rs 2000
- Rs 6000
- Rs 5000
- Rs 8000
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The Correct Option is A
Solution and Explanation
Ratio of profit shares of 'A', 'B' and 'C':
= {(10x × 12) + (10x × 2 × 12)} : {(20x × 6) + (18 × 1.25 × 20x)} : {12 × 5000}
= {120x + 240x} : {120x + 450x}:60000
= 360x : 570x : 60000 = 12x : 19x : 2000
According to the question,
\(\frac{12x}{(31x + 2000)}=(\frac{2400}{10200})\)
Or, 12x × 102 = 24 × (31x + 2000)
Or, 51x = 31x + 2000
Or, 20x = 2000
So, x = 100
So, investment of 'B' = 100 X 20 = Rs. 2,000
So, the correct option is (A) : Rs 2000.
= {(10x × 12) + (10x × 2 × 12)} : {(20x × 6) + (18 × 1.25 × 20x)} : {12 × 5000}
= {120x + 240x} : {120x + 450x}:60000
= 360x : 570x : 60000 = 12x : 19x : 2000
According to the question,
\(\frac{12x}{(31x + 2000)}=(\frac{2400}{10200})\)
Or, 12x × 102 = 24 × (31x + 2000)
Or, 51x = 31x + 2000
Or, 20x = 2000
So, x = 100
So, investment of 'B' = 100 X 20 = Rs. 2,000
So, the correct option is (A) : Rs 2000.
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