Question

Rs. 400 distribute 6 men, 12 ladies and 17 boys in such a way that 2 men get equal amount of 5 boys and 2 women get equal amount of 3 boys. how many rupees have received by a man, a woman and a boy? ​

Answer 1

Answer:

Let the amount given to man = x, boy = y & women = z.

a/q

$6x + 17y + 12z = 400........(i) \\ also \: \: 2x = 5y............(ii) \\ 3y = 2z.........(iii)$

Substituting x & z in terms of y in (i)

$15y + 17y + 18y = 400 \\ 50y = 400 \\ y = 8$

$so \: man \: receive = x = \frac{5}{2} y = \frac{5}{2} \times 8 = 20 \\ boy \: receive = y = 8 \\ women \: receive = z = \frac{3}{2} y = \frac{3}{2} \times 8 = 12$