A total fixed amount of N thousand rupees is given to three persons A, B, C , every year, each being given an amount proportional to her age. In the first year, A got half the total amount. When the sixth payment was made, A got six-seventh of the amount that she had in the first year; B got Rs. 1000 less than that she had in the first year; and C got twice of that she had in the first year. Find N .

Step-by-step solution

Let total amount given each year be N₁ , and the respective ages of persons A, B and C are a, b and c years respectively. The ratio of initial distribution = a : b : c . If k is the ratio coefficient then a k+b k+c k=N₁ k= N₁ a+b+c A.T.Q: a N₁ a+b+c = N₁ 2 a a+b+c = 1 2 ...(i) and b+c a+b+c = 1 2 ...(ii) When 6^ th payment was made then ratio of distribution is a+5: b+5: c+5 . (a+5) k₁+(b+5) k₁+(c+5) k₁=N k₁= N₁ a+b+c+15 Again A.T.Q: N₁(a+5) a+b+c+15 = 6 7 ~N 2 ...(iii) N₁(b+5) a+b+c+15 = b N₁ a+b+c -1000 ...(iv) a