Ram and Lakshman enters into a partnership with capitals in the ratio of 5:6. At the end of 4 months, Ram withdraws. If they receive profits in the ratio of 5:9. Find how long Lakshman's capital was used?
Question
Ram and Lakshman enters into a partnership with capitals in the ratio of 5:6. At the end of 4 months, Ram withdraws. If they receive profits in the ratio of 5:9. Find how long Lakshman's capital was used?
Solution
Let's solve this step by step:
Step 1: Understand the problem The problem is about a partnership where Ram and Lakshman invest in the ratio of 5:6. Ram withdraws his investment after 4 months and the profit ratio is given as 5:9. We need to find out for how long Lakshman's capital was used.
Step 2: Use the formula for profit sharing in a partnership In a partnership, the profit is divided in the ratio of the product of the capital investment and the time period for which the capital was invested.
So, if we denote Ram's investment time as R, Lakshman's investment time as L, and their capital investments as 5x and 6x respectively, we can write the equation for the profit sharing as:
5x * R : 6x * L = 5 : 9
Step 3: Substitute the known values We know that Ram's investment time (R) is 4 months. Substituting this in the equation we get:
5x * 4 : 6x * L = 5 : 9
Step 4: Simplify the equation Simplifying the equation, we get:
20x : 6xL = 5 : 9
Step 5: Solve for L Cross multiplying and solving for L, we get:
L = (20 * 9) / (5 * 6)
L = 6 months
So, Lakshman's capital was used for 6 months.
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