An amount of ₹866 is divided among three persons in the ratio of 2 : 6 : 12. Thedifference between the largest and the smallest shares (in ₹) in the distribution is:

Correct option is C

Given:

Total amount = ₹866

The ratio of the shares among three persons = 2 : 6 : 12

Solution:

Let the shares of the three persons be 2x, 6x, and 12x respectively.

The total amount is the sum of the shares:

2x + 6x + 12x = 866

20x = 866

x =$$\frac{866}{20}$$​ = 43.3

The smallest share = 2x = 2 × 43.3 = 86.6

The largest share = 12x = 12 × 43.3 = 519.6

Difference = 519.6 - 86.6 = 433

Alternate Solution:  

Total share ratio = 2 + 6 + 12 = 20 

20 units = 866 

1 units = $$\frac{866}{20}$$​​

Difference = 12 - 2 = 10 

10 units = $$\frac{866}{20} \times 10 = 433$$​​