Question

A rich farmer died leaving behind a hundred acres of his farm to be divided among his three daughters Rashmi, mala, rekha -in the proportion of one-third, one-fourth and one-fifth. But Rekha died unexpectedly.
Now how should the executor divide the land between Rashmi and Mala in a fair manner?

Answer 1

Give them half each

Answer 2

It is a Ratio- Proportion problem.
Division must be proportionately divided between them.
Case-1
If 3 of daughters alive: They get the share of their property.
Total 100 acres. divided into 12 parts.
1st daughter get share of 100/12 x 5 = 41.67 acres.
2nd daughter get share of 100/12 x 4 = 33.33 acres.
3rd daughter get share of 100/12 x 3 = 25.00 acres.
Case-2
2 daughters alive. 3rd daughter died.
Total 100 acres. divided into 9 parts.
1st daughter get share of 100/9 x 5 = 55.56 acres.
2nd daughter get share of 100/9 x 4 = 44.44 acres.
ANS: executor divide the land between Rashmi (55.56 acres) and Mala (44.44 acres)

Answer 3

Initial ratio is 1/3: 1/4: 1/5
Taking LCM
Ratio = 20/60:15/60:12/60
=20 acres, 15 acres, 12 Acres (Balance 13 acres are not shared among them)
After the death of REKHA, her share of 12 Acres have to be divided in the ratio 20:15:13
Rashmi's share = 12 (20/48) = 5 acres
Mala's share = 12 (15/48) = 3.75
So total RASHMI's share = 20+5=25
Mala's share = 12+3.75 = 15.75=

They have to share in the ratio of 25: 15.75
=100:63