An amount of Rs.130000 is to be shared among 4 singers, 5 dancers, and 3 hosts. It is given that the total sum received by 3 hosts equals that of 2 dancers, and the total sum received by 3 dancers equals that of 2 singers. How much does each singer get?

Explanation

Let the amounts received by a singer, dancer, and host be S, D, and C respectively. Given 3C = 2D and 3D = 2S, so S = (3D)/2 and C = (2D)/3. The total amount is 4S + 5D + 3C = 130000. Substituting, 4*(3D/2) + 5D + 3*(2D/3) = 130000, which simplifies to 6D + 5D + 2D = 130000, or 13D = 130000. Hence, D = 10000 and S = (3*10000)/2 = 15000. Therefore, each singer receives Rs.15000.