₹ 27,600 is distributed among Thomas, David and Vijay in such a manner that $$\frac17^{th}$$​ of the share of Thomas, $$\frac13^{th}$$​ of the share of David and $$\frac12$$​of the share of Vijay are equal. Find the sum of the share of Thomas and Vijay.

Correct option is D

Given:

Total = ₹ 27,600

​$$\frac{1}{7}$$​of Thomas’s share = $$\frac{1}{3}$$​of David’s share = $$\frac{1}{2}$$​ of Vijay’s share (all equal)

Solution:
If $$\frac{1}{7}T=\frac{1}{3}D=\frac{1}{2}V=k$$​, then
T = 7k ; D = 3k; V = 2k and T + D + V = 12k = Total.

12k = 27,600

k=2,300
T=7k$$=7\times2{,}300=16{,}100$$​​
V=2$$k=2\times2{,}300=4{,}600$$​​
T+V=16,100+4,600 = ₹20,700