Question

rs. 600 are divided among a b c so that rs. 40 more than 2/5 th of a???s share rs. 20 more than 2/7 th of b???s share and rs. 10 more than 9/17 th of c???s may all be equal. what is a???s share (in rupees)?

Answer 1

Calculations :

Let contribution of A be a, of B be b and of C be c

From the question we have :

2/5a + 40 = 2/7b + 20 = 9/17c + 10

a + b + c = 600

We can rewrite and combine two unknowns in the following way :

10b - 14a = 700..... i

34b - 63c = 1190....... ii

45c - 34a = 2550....... iii

a + b + c = 600...... iv

Lets obtain the value of a from equation iv. We have :

a = 600 - b - c

Substituting this in iii we have :

45c - {34(600 - b - c)} = 2550

45c + 34c + 34b - 20400 = 2550

79c + 34b = 22950

Solving for C with respect to equation ii we have :

34b + 79c = 22950

34b - 63c = 1190

We subtract the two and get :

142c = 21760

c = 153, 17/71

Substituting this in iii we have :

45 × 153 17/71 - 34a = 2550

34a = 4345 55/71

a = 127 58/71