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₹ 27,600 is distributed among Thomas, David and Vijay in such a manner that 17th\frac17^{th}71​th​ of the share of Thomas, 13th\frac13^{th}31​th​ of t
Question

₹ 27,600 is distributed among Thomas, David and Vijay in such a manner that 17th\frac17^{th}​ of the share of Thomas, 13th\frac13^{th}​ of the share of David and 12\frac12​of the share of Vijay are equal. Find the sum of the share of Thomas and Vijay.

A.

18,720

B.

15,200

C.

16,700

D.

20,700

Correct option is D

Given:

Total = ₹ 27,600

17\frac{1}{7}​of Thomas’s share = 13\frac{1}{3}​of David’s share = 12\frac{1}{2}​ of Vijay’s share (all equal)

Solution:
If 17T=13D=12V=k\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 =7×2,300=16,100=7\times2{,}300=16{,}100 
V = 2k=2×2,300=4,600k=2\times2{,}300=4{,}600​​
T + V = 16,100 + 4,600 = ₹20,700

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