While trading, Amit invested thrice the amount invested by Asif. From first day onwards, Amit loses an amount equal to ‘k’ on each day, and at the same time Asif gains half of what Amit loses each day. At the end of the third day, the ratio of amount of money with Amit and Asif is 9 : 8. On which day after 3rd day would the ratio be 1 : 2
Question
While trading, Amit invested thrice the amount invested by Asif. From first day onwards, Amit loses an amount equal to ‘k’ on each day, and at the same time Asif gains half of what Amit loses each day. At the end of the third day, the ratio of amount of money with Amit and Asif is 9 : 8. On which day after 3rd day would the ratio be 1 : 2
Solution
Let's denote the initial amount of money invested by Asif as 'A' and the amount of money invested by Amit as '3A' (since Amit invested thrice the amount invested by Asif).
On each day, Amit loses 'k' amount of money and Asif gains half of what Amit loses, which is 'k/2'.
So, after 3 days:
- Amit's amount = 3A - 3k
- Asif's amount = A + 3*(k/2) = A + 3k/2
According to the problem, at the end of the third day, the ratio of the amount of money with Amit and Asif is 9:8. So we can write this as:
(3A - 3k) / (A + 3k/2) = 9/8
Solving this equation, we find that k = A/2.
Now, we want to find out on which day after the 3rd day would the ratio be 1:2.
Let's denote the number of days after the 3rd day as 'd'. So, the equation becomes:
(3A - (3+d)k) / (A + (3+d)k/2) = 1/2
Substituting k = A/2 into the equation, we get:
(3A - (3+d)A/2) / (A + (3+d)A/4) = 1/2
Solving this equation, we find that d = 5.
So, the ratio of the amount of money with Amit and Asif would be 1:2 on the 5th day after the 3rd day, which is the 8th day.
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