A man's inheritance money = $1200
Given :
He shared his inheritance between his 3 sons in the ratio 1:3:6
Then, the money the first son got :
![= \tt \frac{1}{10} \: of \: 1200](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20%5Cfrac%7B1%7D%7B10%7D%20%20%5C%3A%20of%20%20%5C%3A%201200)
![=\tt \frac{1}{10} \times 1200](https://tex.z-dn.net/?f=%20%3D%5Ctt%20%20%5Cfrac%7B1%7D%7B10%7D%20%20%5Ctimes%201200)
![=\tt \frac{1 \times 120}{10}](https://tex.z-dn.net/?f=%20%3D%5Ctt%20%20%5Cfrac%7B1%20%5Ctimes%20120%7D%7B10%7D%20)
![= \tt \frac{1200}{10}](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20%5Cfrac%7B1200%7D%7B10%7D%20)
![\color{plum} =\tt\$ \: 120](https://tex.z-dn.net/?f=%5Ccolor%7Bplum%7D%20%3D%5Ctt%5C%24%20%5C%3A%20120)
▪︎Thus, the first son inherited $120.
Money the second son got :
![= \tt \frac{3}{10} \: of \: 1200](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20%5Cfrac%7B3%7D%7B10%7D%20%20%5C%3A%20of%20%20%5C%3A%201200%20)
![= \tt \frac{3}{10} \times 1200](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20%5Cfrac%7B3%7D%7B10%7D%20%20%5Ctimes%201200)
![=\tt \frac{3 \times 1200}{10}](https://tex.z-dn.net/?f=%20%3D%5Ctt%20%20%5Cfrac%7B3%20%5Ctimes%201200%7D%7B10%7D%20)
![= \tt \frac{3600}{10}](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20%5Cfrac%7B3600%7D%7B10%7D%20)
![\color{plum} =\tt \$360](https://tex.z-dn.net/?f=%5Ccolor%7Bplum%7D%20%3D%5Ctt%20%5C%24360)
▪︎Thus, the second son inherited $360.
Money the third son got :
![=\tt \frac{6}{10} \: of \: 1200](https://tex.z-dn.net/?f=%20%3D%5Ctt%20%20%5Cfrac%7B6%7D%7B10%7D%20%20%5C%3A%20of%20%20%5C%3A%201200)
![=\tt \frac{6}{10} \times 1200](https://tex.z-dn.net/?f=%20%3D%5Ctt%20%20%5Cfrac%7B6%7D%7B10%7D%20%20%5Ctimes%201200)
![= \tt \frac{6 \times 1200}{10}](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20%5Cfrac%7B6%20%5Ctimes%201200%7D%7B10%7D%20)
![= \tt \frac{7200}{10}](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20%5Cfrac%7B7200%7D%7B10%7D%20)
![\color{plum} = \tt\$720](https://tex.z-dn.net/?f=%5Ccolor%7Bplum%7D%20%3D%20%5Ctt%5C%24720)
▪︎Thus, the third son inherited $720.
We know that :
The largest share = $720
The smallest share = $120
Difference between the largest and smallest share :
![= \tt720 - 120](https://tex.z-dn.net/?f=%20%3D%20%5Ctt720%20-%20120)
![\color{hotpink}\tt = 600](https://tex.z-dn.net/?f=%5Ccolor%7Bhotpink%7D%5Ctt%20%3D%20600)
<h3> ●=> Therefore :</h3>
▪︎<em>The difference between the largest and smallest share = 600</em>