Deepak, Eknath and Falguni got a sizeable amount of inheritance from their
father who had just passed away. However, the sums they received were not
equal. The siblings were fond of each other. Deepak being the eldest decided to
give away ¼ of his share to Eknath. This spurred Eknath into action too and he
gave away 1/3 of what he had to Falguni after receiving the gift from Deepak.
Now all of them had the same amount and everyone was happy. If the total
amount that their father had distributed was Rs. 2,70,000, how much had each
received from their father originally?
Let's calculate step-by-step:
1. Let's assume that Deepak received x rupees from their father.
2. Thus, Eknath received (1/4)x rupees from Deepak.
3. After receiving this gift, Eknath's total is now (1 + 1/4)x rupees.
4. Therefore, Eknath's total after receiving the gift is (5/4)x rupees.
5. Eknath then gives away 1/3 of his total to Falguni, which means he gives away (1/3)(5/4)x rupees.
6. After giving away the amount, Eknath has (5/4)x - (1/3)(5/4)x = (5/4)x - (5/12)x = (25/12)x rupees left.
7. Since all three siblings have the same amount in the end, this amount is equal to (25/12)x rupees.
8. The total amount distributed by their father was Rs. 2,70,000. So we have: (25/12)x = 2,70,000.
9. Now, we can solve for x: x = (2,70,000 * 12)/25.
Therefore, each sibling received the following amounts originally:
Deepak: x rupees
Eknath: (5/4)x rupees
Falguni: (25/12)x rupees
To solve this problem, let's work backwards.
Let's assume that after all the exchanges, each sibling received "x" amount of money.
According to the given information, we know that Deepak initially had 4 times the amount he gave to Eknath. So, Deepak received 4x.
Similarly, Eknath received 3 times the amount he gave to Falguni. So, Eknath received 3x.
And Falguni received the remaining amount, which is x.
Now, we can sum up all the amounts received by each sibling:
4x + 3x + x = 270000
Combining like terms, we get:
8x = 270000
Dividing both sides by 8, we find:
x = 33750
So, each sibling initially received the following amounts:
Deepak: 4x = 4 * 33750 = 135000
Eknath: 3x = 3 * 33750 = 101250
Falguni: x = 33750
Therefore, Deepak received Rs. 1,35,000, Eknath received Rs. 1,01,250, and Falguni received Rs. 33,750 from their father initially.