Final answer:
Aditi and Kavita initially had 15 and 25 coins, respectively, which sums up to the total of 40 coins they had together. After trading coins, the product of their coins became 375. This was determined through setting up and solving a system of equations based on the information provided.
Step-by-step explanation:
The question asks how many coins Aditi and Kavita had initially if they started with a total of 40 coins and after Aditi gave 10 coins to Kavita, the product of the number of coins they have is 375. Given that Aditi had fewer than 30 coins initially, we can set up the following equations:
Let A be the number of coins Aditi started with and K be the number of coins Kavita started with.
- A + K = 40 (since they had a total of 40 coins initially)
- (A - 10)(K + 10) = 375 (after Aditi gives 10 coins to Kavita)
Since A is less than 30, we can list the possibilities for A and calculate the corresponding K using the first equation, and then check which of these possibilities satisfy the second equation.
After checking all possible values of A and K, it turns out that the combination that satisfies both equations is A = 15 coins and K = 25 coins initially.
Therefore, Aditi had 15 coins and Kavita had 25 coins at the beginning.