Question

Divide 1260 among A B C so that the ratio between the shares of A and B is 2:3 and the ratio between B and C is 4:5

Answer 1

so the resultant ratio of A,B,C will be 8:12:15

Answer 2

$\frac{a}{b} = \frac{2}{3} \: \: and \: \: \frac{b}{c} = \frac{4}{5} \\ b = \frac{4}{5}c \: \: and \: \: a = \frac{2}{3}b = \frac{2}{3} \times \frac{4}{5} c = \frac{8}{15} c \\ a + b + c = 1260 \\ \frac{8}{15} c + \frac{4}{5}c + c = 1260 \\ \frac{8c + 12c + 15c}{15} = 1260 \\ 35c = 1260 \times 15 \\ c = 1260 \times 15 \div 35 \\ = 180 \times 3 \\ = 540 \\ b = 4 \times 540 \div 5 = 432 \\ a = 8 \times 540 \div 15 = 36 \times 8 = 288$